📝 Exam Questions — Mechanics 1

Motion in a straight line can be represented graphically. (a) State two types of graphs commonly used to represent motion in a straight line. [2] (b) Sketch a displacement-time graph for an object moving with constant positive velocity. [3]

A rocket launches vertically upwards from rest. It accelerates uniformly to a velocity of 150 m s⁻¹ in the first 5 seconds. After this, its engines cut out, and it continues to move upwards under gravity, reaching its maximum height at 15 seconds from launch. Assume g = 9.81 m s⁻². (a) Calculate the acceleration of the rocket in the first 5 seconds. [3] (b) Determine the average acceleration of the rocket during the entire 15 seconds. [5]

The velocity-time graph in Fig 1.1 shows the motion of a particle moving in a straight line over a 6-second period. (a) Determine the direction of the velocity during the time interval 0 to 2 seconds and 4 to 6 seconds. [4] (b) State the time interval(s) during which the object is momentarily at rest. [3]

A particle moves in a straight line. The velocity-time graph for the particle's motion is shown in Fig 1.1. (a) Analyse the motion of the particle, describing its movement in terms of direction and changes in speed. [6] (b) Deduce the position of the particle at t = 6 s, assuming it starts from the origin. Show your working. [6]

Fig 1.1 shows a velocity-time graph for a car travelling in a straight line. (a) Calculate the total displacement of the car during the 10 seconds. [4] (b) Identify the time interval during which the car is moving with constant velocity. [2]

Fig 1.2 shows a velocity-time graph for a train's motion. (a) Show that the total distance travelled by the train in the first 20 seconds is 150 m. [4] (b) Calculate the total displacement of the train after 30 seconds. [5]

Fig 1.1 shows a velocity-time graph for a particle moving in a straight line. (a) Analyse the motion of the particle in each segment of the graph. [5] (b) Sketch the corresponding acceleration-time graph for the particle's journey from t = 0 s to t = 25 s. [7]

Fig. 1.2 shows the velocity-time graph for a particle moving in a straight line for a total of 12 seconds. (a) Calculate the average speed for the first 8 seconds of the motion. [4] (b) Determine the average velocity for the entire 12-second journey. [4] (c) Evaluate the significance of the point where the velocity becomes zero on the graph. [4]

When analysing the motion of objects, physicists use a variety of quantities. Understanding the nature of these quantities is fundamental. (a) Discuss why it is crucial to distinguish between scalar and vector quantities when describing motion in physics. [6] (b) Identify a common misconception students have regarding scalar and vector quantities and suggest how it can be addressed. [4]

When describing motion in a straight line, it is essential to define a positive direction. Fig 1.1 illustrates a standard convention for this. **Fig 1.1** (a) Identify the positive direction as indicated on the diagram. [2] (b) Identify the direction of movement if an object has a velocity of -3 m s⁻¹. [2]

A car travels along a straight road from town A to town B. (a) Calculate the average speed of the car if it travels a total distance of 120 km in 2 hours. [4] (b) Explain why the average velocity for the same car might be different from its average speed if the journey involved a return trip from town A to town B and back to town A. [4]

In mechanics, precise language and notation are crucial for clear communication of physical quantities. (a) State the SI unit for displacement. [2] (b) Give the standard notation for initial velocity and final velocity. [2]

In the study of motion in a straight line, it is essential to define an origin and a positive direction to describe an object's position. (a) Describe what a 'negative position' means relative to an origin and a chosen positive direction. [3] (b) Illustrate this concept with a simple diagram, marking the origin, positive direction, and a point of negative position. [3]

The study of motion requires a clear understanding of fundamental quantities and their units. (a) Derive the SI units for acceleration from the definition of average acceleration. [5] (b) Explain why the unit 'm s⁻²' is preferred over 'm/s/s'. [3]

In the study of motion, 'distance' and 'displacement' are key concepts. (a) Distinguish between 'distance' and 'displacement'. [3] (b) Give the SI units for distance and displacement. [2]

An object's motion is represented by the velocity-time graph shown in Fig. 1.3. (a) Calculate the average speed of the object during the first 6 seconds. [4] (b) Calculate the average velocity of the object during the first 6 seconds. [3] (c) Discuss why the values for average speed and average velocity are different in this case. [3]

An object moves in a straight line. Its motion can be described by its instantaneous velocity. (a) Define instantaneous velocity. [2] (b) Explain why instantaneous velocity is a vector quantity. [2]

In the study of motion, quantities are categorised as either scalar or vector. (a) Identify whether 'speed' is a scalar or vector quantity, and justify your answer. [3] (b) Distinguish between 'velocity' and 'acceleration' in terms of their definitions and units. [3]

A car travels 120 km due east in 2.0 hours, then turns around and travels 30 km due west in 0.5 hours. (a) Calculate the total distance travelled by the car. [3] (b) Calculate the average speed of the car for the entire journey. [2] (c) Determine the average velocity of the car for the entire journey. [3]

In physics, quantities used to describe motion can be classified as either scalar or vector quantities. (a) Explain the key difference between a scalar quantity and a vector quantity. [3] (b) Give two examples of vector quantities and for each, briefly describe its significance in motion. [4]

A particle moves in a straight line, starting from rest. Its motion involves periods of acceleration, constant velocity, and deceleration. (a) Compare instantaneous speed and instantaneous velocity, highlighting their similarities and differences. [4] (b) Sketch a displacement-time graph and a velocity-time graph on separate axes for a particle that starts from rest, accelerates uniformly for a short period, then moves at constant velocity, and finally decelerates uniformly back to rest. [7]

When describing motion along a straight line, such as a car moving along a road or a ball rolling on a flat surface, the concept of direction is crucial. (a) Explain why it is necessary to define a positive direction when analysing motion in a straight line. [4] (b) Describe how the choice of positive direction affects the signs of displacement and velocity for an object moving along a straight line. [4]

A runner completes a training session on a circular track. (a) Discuss why the average speed and average velocity of the runner might be different for a given period of time. [4] (b) Explain how a runner could have a non-zero average speed but a zero average velocity over a period of time. [6]

A particle moves from point A to point B. (a) Sketch a simple diagram illustrating the path of a particle moving from point A to point B along a curved path. [3] (b) On your diagram, label the distance travelled and the displacement of the particle. [3]

A car is travelling along a straight road. (a) Define acceleration. [2] (b) State the SI unit for acceleration and whether it is a scalar or vector quantity. [3]

Fig 1.3 shows a velocity-time graph for an object moving in a straight line over an 8-second period. (a) Calculate the total distance travelled by the object. [4] (b) Determine the average velocity of the object over the entire 8-second period. [3]

An object moves in a straight line, and its motion is represented by the velocity-time graph shown in Fig. 1.1. (a) Determine the velocity of the object at t = 2 s and at t = 8 s from Fig. 1.1. [4] (b) State what a horizontal line on a velocity-time graph represents. [3]

A cyclist completes a journey. Throughout the journey, the cyclist's speed varies. (a) Define average speed. [2] (b) State the difference between average speed and average velocity. [3]

A particle moves along a straight line. A positive direction has been defined for its motion. (a) Compare the implications of an object having a negative velocity versus a negative acceleration, considering the predefined positive direction. [5] (b) Discuss a scenario where an object has negative velocity but positive acceleration, explaining the resulting motion. [6]

Physics calculations require careful attention to units. (a) Convert a speed of 72 km/h into m/s. [3] (b) Explain why it is important to use consistent units in physics calculations. [3]

A car travels along a straight road. Its motion can be described in terms of how fast it is moving and in what direction. (a) Define speed. [2] (b) State the key difference between speed and velocity. [3]

In the study of motion, quantities are categorised as either scalar or vector. (a) Define the term 'scalar quantity'. [2] (b) State three examples of scalar quantities commonly used in mechanics. [3]

An object moves in a straight line. (a) Define the term 'displacement'. [2] (b) Calculate the distance travelled by an object with a constant speed of 15 m s⁻¹ for 5 seconds. [2]

A runner completes a 400 m race. They accelerate uniformly from rest for 5 seconds, reaching a maximum speed of 8 m/s. They maintain this speed for a further 30 seconds before decelerating uniformly to a stop in 5 seconds. (a) Draw a velocity-time graph for the runner's motion, labelling all significant points. [5] (b) Calculate the total displacement of the runner. [4] (c) Explain how the graph would change if the runner had decelerated over a shorter time period at the end of the second phase. [2]

A car's motion is represented by the speed-time graph shown in Fig. 1.4. (a) Interpret the motion of the object between t=5 s and t=10 s from Fig. 1.4. [3] (b) Calculate the total distance travelled by the object from t=0 s to t=10 s. [4]

Fig 1.1 shows a velocity-time graph for a car's journey. (a) Calculate the total distance travelled by the car. [4] (b) Calculate the average speed of the car for the entire journey. [2] (c) Interpret the significance of the negative velocity shown in the graph. [3]

A car accelerates from an initial velocity of 15 m s⁻¹ to a final velocity of 5 m s⁻¹ in a straight line over a period of 4 seconds. (a) Calculate the acceleration of the car. [3] (b) Explain what a negative acceleration implies about the car's motion. [4]

Understanding how to interpret graphs is crucial in mechanics. (a) State what the area under a velocity-time graph represents. [2] (b) Calculate the displacement of an object that moves at a constant velocity of 5 m s⁻¹ for 10 seconds. [3]

A ball is dropped from rest from a height of 20 m. Assume air resistance is negligible and the acceleration due to gravity is 9.81 m s⁻². (a) Calculate the instantaneous velocity of the ball just before it hits the ground. [3] (b) Compare this instantaneous velocity with its average velocity during the fall. [3]

Fig 1.3 shows a velocity-time graph for an object's motion. (a) Derive the formula for the area of a trapezium, given its parallel sides are velocities V₁ and V₂ and the time interval is T, relating it to displacement. [4] (b) Explain why, for a velocity-time graph, the total distance travelled may differ from the final displacement. [3] (c) Calculate the average speed of the object over the entire 12-second journey shown in Fig 1.3. [4]

Fig. 1.2 shows the displacement-time graph for an object moving in a straight line. (a) Analyse the features of the displacement-time graph in Fig. 1.2 that indicate a change in velocity. [4] (b) Sketch the corresponding velocity-time graph for the motion shown in Fig. 1.2. [3] (c) Calculate the average velocity of the object over the entire 15 s journey from the displacement-time graph. [3]

The motion of an object is represented by the velocity-time graph shown in Fig 1.1. (a) Calculate the displacement of the object from its initial position at t = 5 s. [4] (b) Compare the total distance travelled by the object with its displacement at t = 5 s. [3]

A ball is thrown vertically upwards from the ground. It leaves the hand with an initial velocity of 15 m s⁻¹ and experiences a constant downward acceleration due to gravity of 10 m s⁻². Assume upwards is the positive direction. (a) Draw a velocity-time graph for the ball's motion from the moment it leaves the hand until it hits the ground. Mark the key values on your axes. [3] (b) Calculate the displacement of the ball from its starting point after 5 seconds. [5]

Fig 1.2 shows a displacement-time graph for an object moving in a straight line. (a) Calculate the instantaneous velocity of the object at t = 5 s. [3] (b) Calculate the instantaneous velocity of the object at t = 15 s. [3] (c) Identify the time interval(s) during which the object is at rest. [2]

Fig 1.2 shows a velocity-time graph for a cyclist. (a) Calculate the acceleration of the cyclist during the first 10 seconds. [3] (b) Calculate the acceleration of the cyclist between t = 20 s and t = 30 s. [3] (c) Describe the motion of the cyclist between t = 10 s and t = 20 s. [3]

An object's motion can be described in terms of its displacement, velocity, and acceleration. These are all vector quantities. (a) Discuss the importance of specifying a positive direction when working with vector quantities in mechanics. [6] (b) Determine the resultant displacement of an object that moves 5 km East, then 3 km West, assuming East is the positive direction. [4]

When describing motion, it is important to distinguish between different types of physical quantities. (a) Explain the difference between scalar and vector quantities, using examples relevant to motion. [4] (b) Identify which of the following are vector quantities: speed, distance, velocity, acceleration. [3]

A train travels in a straight line. It moves for 40 seconds at a constant velocity of 20 m s⁻¹ in the positive direction. It then reverses direction and travels for 60 seconds at a constant velocity of 10 m s⁻¹. The total duration of the motion is 100 seconds. (a) Calculate the total distance travelled by the train during the 100 seconds. [5] (b) Explain why the magnitude of the displacement is less than the total distance travelled in this scenario. [4]

Fig. 1.1 shows the velocity-time graph for an object moving in a straight line. (a) Describe the motion of the object shown in Fig. 1.1 from t=0 s to t=10 s. [3] (b) Calculate the displacement of the object from t=0 s to t=10 s. [5]

Fig 1.6 shows a velocity-time graph for an object moving in a straight line. The velocity values at various times are given in the table below:

(a) Calculate an estimate for the distance travelled using the trapezium rule with 4 equal intervals. [4] (b) Assume an estimate using 2 equal intervals for the same data yielded a result of 60 m. Compare the accuracy of using 2 intervals versus 4 intervals for this estimation, and discuss why the difference might be significant. [5]

Fig 1.2 shows a velocity-time graph for an object moving in a straight line. (a) Discuss the advantages and disadvantages of using graphical estimation methods compared to analytical integration, assuming the velocity function is known. [4] (b) Calculate an estimate for the total distance travelled by the object from t=0s to t=8s, using the trapezium rule with intervals of 2 seconds. [5] (c) Justify whether this estimate is likely to be an overestimate or an underestimate of the actual distance travelled. [3]

Fig 1.5 shows the velocity-time graph for an object moving in a straight line. (a) Estimate the total displacement of the object from t=0s to t=10s using the counting squares method. [4] (b) Explain one potential source of error in your estimation. [2]

A car accelerates from rest, reaching a velocity of 10 m s⁻¹ after 4 seconds. It then continues to accelerate, reaching 15 m s⁻¹ after a further 4 seconds (total time 8 seconds). The acceleration is not constant during either interval. (a) Sketch a velocity-time graph for the car's motion. [3] (b) Estimate the total distance travelled by the car using the trapezium rule with two equal time intervals. [3] (c) Suggest how the accuracy of the estimation could be improved. [2]

When analysing motion, it is sometimes necessary to determine displacement from a velocity-time graph where the velocity changes non-linearly. (a) Describe one method for estimating the area under a non-linear velocity-time graph. [3] (b) State why estimation methods are sometimes necessary for such graphs. [2]

Fig 1.4 shows a speed-time graph for a runner during a 10-second sprint. (a) Estimate the total distance travelled by the runner from t=0s to t=10s using the trapezium rule with 5 equal intervals. [5] (b) Comment on the accuracy of this estimation given the shape of the graph. [2]

Fig 1.1 shows a velocity-time graph for a rocket during its initial ascent. (a) Estimate the displacement of the rocket during the first 6 seconds using the mid-ordinate rule with 3 equal strips. [4] (b) Analyse how the choice of estimation method (e.g., trapezium rule vs. mid-ordinate rule) might affect the accuracy for this specific curve. [3] (c) Evaluate the limitations of using graphical methods to determine exact displacement. [3]

Fig 1.4 shows two velocity-time graphs on the same axes for Cyclist A and Cyclist B, both starting from rest. (a) Analyse the motion of the two cyclists, A and B, by describing their acceleration and deceleration phases. [5] (b) Compare the total displacement of Cyclist A and Cyclist B after 20 seconds. [4] (c) Evaluate which cyclist had the greater average speed over the first 15 seconds. [3]

Fig 1.2 shows a diagram of a marble's motion along a straight line. The origin is at 0 m, and the positive direction is to the right. (a) Determine the initial and final positions of the marble from the diagram. [2] (b) Calculate the total distance travelled by the marble shown in the diagram. [2] (c) Calculate the displacement of the marble from its starting point to its final point. [2]

Fig 1.16 shows Hinesh's speed-time graph. (a) Calculate the average acceleration of Hinesh during the first 5 minutes of his journey. (b) Describe Hinesh's motion between t = 5 min and t = 20 min.

Fig 1.16 shows Hinesh's speed-time graph for a 30-minute journey. (a) Calculate the distance Hinesh travels in the first 10 minutes. [3] (b) Calculate Hinesh's average speed for the entire 30-minute journey. [3] (c) State the total time Hinesh spent travelling at a constant speed. [3]

Fig 1.12 shows a velocity-time graph for a marble. (a) Calculate the initial velocity of the marble. (b) Determine the final velocity of the marble at t = 2.0 s. (c) Calculate the average acceleration of the marble over the entire 2-second interval.

Fig 1.6 shows a position-time graph of Amy's journey, with home as the origin. (a) Determine Amy's position at t = 10 min and at t = 30 min from the graph. (b) Calculate Amy's average velocity for the entire journey shown on the graph. (c) Calculate Amy's average speed for the entire journey shown on the graph.

Fig 1.20 shows Sunil's velocity-time graph for a 10-second journey. (a) Calculate Sunil's displacement from t = 0 s to t = 6 s. [3] (b) Calculate Sunil's final displacement at t = 10 s. [4] (c) Compare the total distance travelled with the final displacement for Sunil's journey, explaining any difference. [3]

Fig 1.1 illustrates the position of a marble relative to a hand. The hand is at the zero position, and the positive direction is upwards. (a) State the initial positive position of the marble shown in Fig 1.1. [1] (b) The marble then moves to a new position of -0.5 m. Calculate the displacement of the marble. [2] (c) Explain the meaning of a negative position value in the context of this diagram. [2]

Fig 1.19 shows Sunil's speed-time graph for a 10-second journey. (a) Calculate Sunil's total distance travelled during the 10 seconds. [3] (b) Calculate Sunil's average speed for the entire journey. [3] (c) Determine the maximum speed Sunil reaches during his journey. [2]

Fig 1.12 shows the velocity-time graph for a marble moving in a straight line. (a) Calculate the displacement of the marble between t = 0 s and t = 2 s. (b) Calculate the total distance travelled by the marble between t = 0 s and t = 2 s. (c) Determine the time at which the marble momentarily stops.

Fig 1.11 shows a speed-time graph illustrating Tom's cycle journey. (a) Calculate the total distance Tom travelled during his journey. [3] (b) Calculate Tom's average speed for the entire 70-second journey. [4] (c) Sketch the corresponding acceleration-time graph for Tom's journey. [3]

Fig 1.11 shows a speed-time graph illustrating Tom's cycle journey. (a) Calculate Tom's acceleration during the first 10 seconds. [2] (b) Determine the time interval during which Tom cycles at a constant speed. [2] (c) Calculate Tom's deceleration during the last 20 seconds of his journey. [2] (d) Describe the overall motion of Tom's cycle journey as shown in the graph. [3]

Fig 1.4 shows Amy's journey. Home is the origin (0 km), and East is defined as the positive direction. (a) State Amy's initial position relative to home from the diagram. [1] (b) Calculate the total distance Amy travels in the first 20 minutes. [2] (c) Calculate Amy's displacement from home after 30 minutes. [2]

Fig 1.12 shows the velocity-time graph for a marble moving in a straight line. (a) Calculate the acceleration of the marble between t = 0 s and t = 1 s. (b) Calculate the acceleration of the marble between t = 1 s and t = 2 s. (c) Explain what the negative acceleration means in this context.

Fig 1.8 shows the distance-time graph of Amy's journey. (a) Determine the total distance Amy has travelled by t = 20 min from the graph. (b) Calculate Amy's total distance travelled for the entire journey shown. (c) Explain why the position-time graph (Figure 1.6) and the distance-time graph (Figure 1.8) differ for Amy's journey after t = 10 min.

Fig 1.7 shows a velocity-time graph of Amy's journey. (a) Identify the time interval when Amy has the greatest speed. (b) Calculate Amy's speed during the first 10 minutes. (c) Calculate Amy's velocity during the interval from t = 20 min to t = 30 min. (d) Compare Amy's velocity at t = 5 min and t = 25 min, providing quantitative values.

Fig 1.15 shows the speed-time graph for a falling stone. (a) Determine the speed of the falling stone at t = 1.0 s from the graph. (b) Calculate the acceleration of the stone between t = 0 s and t = 2.0 s. (c) Explain why the speed-time graph is a straight line, given the context of a falling stone.

The graph in Fig 1.22 shows the variation of speed with time for a train journey. (a) Calculate the total distance travelled by the train during its 100-second journey. [4] (b) Determine the average speed of the train for the entire journey. [4] (c) Explain why the average speed and average velocity would be the same for this journey, assuming it's in a straight line. [4]

The graph in Fig 1.10 shows the variation of velocity with time for a marble. (a) Calculate the acceleration of the marble at t = 1.0 s from Figure 1.10. (b) Interpret the meaning of the constant gradient in Figure 1.10.

The graph in Fig 1.3 shows the variation of position with time for a marble. The position is measured relative to hand level. (a) Read the initial position of the marble at t = 0 s from the graph. [1] (b) Calculate the displacement of the marble between t = 0 s and t = 4 s. [2] (c) Calculate the average velocity of the marble between t = 0 s and t = 8 s. [3] (d) Describe the motion of the marble between t = 4 s and t = 8 s based on the graph. [2]

Fig 1.3 shows a diagram of a marble's motion with an arrow indicating direction and relevant distances. (a) Identify the direction of the marble's initial movement from Figure 1.3. [1] (b) Explain what causes the marble to change its direction of motion. [2] (c) State the final direction of the marble's movement relative to the origin. [2]

Fig 1.6 shows a position-time graph of Amy's journey, with home as the origin. Fig 1.7 shows a velocity-time graph of Amy's journey. (a) Compare the information presented in Figure 1.6 (position-time) and Figure 1.7 (velocity-time) for Amy's journey between t = 0 min and t = 20 min. (b) Explain how the gradient of Figure 1.6 relates to the values in Figure 1.7. (c) Sketch a possible acceleration-time graph for Amy's journey based on Figure 1.7.

Fig 1.6 shows a position-time graph of Amy's journey, with home as the origin. (a) Calculate Amy's velocity during the first 10 minutes from the graph. (b) Determine the time interval during which Amy is stationary. (c) Calculate Amy's velocity between t = 20 min and t = 30 min. (d) Sketch the corresponding velocity-time graph for Amy's journey based on Figure 1.6.

The graph in Fig 1.22 shows the variation of speed with time for a train journey. (a) Calculate the train's acceleration during the first 20 seconds. [2] (b) Determine the maximum speed reached by the train. [2] (c) Calculate the train's deceleration between t = 80 s and t = 100 s. [2] (d) Describe the motion of the train between t = 20 s and t = 80 s. [3]

The graph in Fig 1.10 shows the variation of velocity with time for a marble. (a) Calculate the average velocity of the marble between t = 0 s and t = 1.0 s from Figure 1.10. [3] (b) Calculate the average speed of the marble between t = 0 s and t = 1.0 s from Figure 1.10. [3] (c) Compare the average velocity and average speed over the first second, explaining why they are different or similar. [2]

The graph in Fig 1.10 shows the variation of velocity with time for a marble moving in a straight line. (a) Determine the instantaneous velocity of the marble at t = 0.5 s from the graph. [2] (b) Explain what the negative velocity indicates at t = 1.5 s. [3] (c) Calculate the average acceleration of the marble between t = 0.5 s and t = 1.5 s. [3]

Fig 1.9 shows a position-time graph for a marble moving in a straight line. (a) Estimate the instantaneous velocity of the marble at time t = 1.0 s by drawing a tangent to the curve at point P. [4] (b) Explain how the slope of the position-time graph relates to the marble's velocity. [3] (c) Compare the marble's velocity at t = 0.5 s and t = 1.5 s, stating whether it is increasing or decreasing. [3]

Fig 1.1 illustrates the position of a marble relative to a hand. (a) State the SI unit for position as shown in Figure 1.1. (b) Identify the origin in Figure 1.1. (c) State the numerical value of the positive position shown in Figure 1.1 and its unit.