Cheat Sheet

Mechanics 1 · Motion in a straight line

Key Facts

Define and differentiate between scalar and vector quantities.

Explain the concepts of distance, position, and displacement.

Interpret and draw position-time, distance-time, speed-time, and velocity-time graphs.

Calculate speed, velocity, and acceleration from given data or graphs.

Distinguish between average speed and average velocity.

Determine displacement and distance travelled from the area under velocity-time and speed-time graphs.

Solve problems involving motion in a straight line with constant acceleration.

Apply appropriate SI units for physical quantities related to motion.

Formulas

Average speed

average speed = \frac{total distance travelled}{total time taken}

average speed

— average speed (m s⁻¹)

total time taken

— total time taken (s)

total distance travelled

— total distance travelled (m)

Used to calculate the overall speed over a journey, irrespective of direction changes. It is a scalar quantity.

Average velocity

average velocity = \frac{displacement}{time taken}

time taken

— time taken (s)

displacement

— displacement (m)

average velocity

— average velocity (m s⁻¹)

Used to calculate the overall velocity over a journey, considering the net change in position. It is a vector quantity.

Average acceleration

average acceleration = \frac{change in velocity}{time taken}

time taken

— time taken (s)

change in velocity

— change in velocity (m s⁻¹)

average acceleration

— average acceleration (m s⁻²)

Used to calculate the overall rate of change of velocity over a period of time. It is a vector quantity.

Area of a rectangle (under speed-time graph)

area = V T

T

— time (s)

V

— speed (m s⁻¹)

Represents the distance travelled when speed is constant.

Area of a trapezium (under speed-time graph)

area = \frac{1}{2} (V_{1} + V_{2}) T

T

— time (s)

V_{1}

— initial speed (m s⁻¹)

V_{2}

— final speed (m s⁻¹)

Represents the distance travelled when speed changes uniformly.

Area of a triangle (under speed-time graph)

area = \frac{1}{2} V T

T

— time (s)

V

— final speed (m s⁻¹)

Represents the distance travelled when speed increases uniformly from rest.

⚠ Common Misconceptions

Students often confuse scalar and vector quantities, particularly distance/displacement and speed/velocity.

Students may think that negative velocity always means slowing down, but it only indicates movement in the negative direction.

Students often believe acceleration only refers to speeding up, but it includes any change in velocity, such as slowing down (deceleration) or changing direction.

Students might assume the origin must be the starting point of motion, rather than any chosen fixed reference point.

Students sometimes fail to specify the positive direction when dealing with vector quantities, leading to ambiguity in signs.

Students may incorrectly interpret the area under a velocity-time graph as total distance instead of displacement, especially when velocity is negative.

Cheat Sheet

Mechanics 1 · Motion in a straight line

Key Facts

Define and differentiate between scalar and vector quantities.

Explain the concepts of distance, position, and displacement.

Interpret and draw position-time, distance-time, speed-time, and velocity-time graphs.

Calculate speed, velocity, and acceleration from given data or graphs.

Distinguish between average speed and average velocity.

Determine displacement and distance travelled from the area under velocity-time and speed-time graphs.

Solve problems involving motion in a straight line with constant acceleration.

Apply appropriate SI units for physical quantities related to motion.

Formulas

Average speed

average speed = \frac{total distance travelled}{total time taken}

average speed

— average speed (m s⁻¹)

total time taken

— total time taken (s)

total distance travelled

— total distance travelled (m)

Used to calculate the overall speed over a journey, irrespective of direction changes. It is a scalar quantity.

Average velocity

average velocity = \frac{displacement}{time taken}

time taken

— time taken (s)

displacement

— displacement (m)

average velocity

— average velocity (m s⁻¹)

Used to calculate the overall velocity over a journey, considering the net change in position. It is a vector quantity.

Average acceleration

average acceleration = \frac{change in velocity}{time taken}

time taken

— time taken (s)

change in velocity

— change in velocity (m s⁻¹)

average acceleration

— average acceleration (m s⁻²)

Used to calculate the overall rate of change of velocity over a period of time. It is a vector quantity.

Area of a rectangle (under speed-time graph)

area = V T

T

— time (s)

V

— speed (m s⁻¹)

Represents the distance travelled when speed is constant.

Area of a trapezium (under speed-time graph)

area = \frac{1}{2} (V_{1} + V_{2}) T

T

— time (s)

V_{1}

— initial speed (m s⁻¹)

V_{2}

— final speed (m s⁻¹)

Represents the distance travelled when speed changes uniformly.

Area of a triangle (under speed-time graph)

area = \frac{1}{2} V T

T

— time (s)

V

— final speed (m s⁻¹)

Represents the distance travelled when speed increases uniformly from rest.

⚠ Common Misconceptions

Students often confuse scalar and vector quantities, particularly distance/displacement and speed/velocity.

Students may think that negative velocity always means slowing down, but it only indicates movement in the negative direction.

Students often believe acceleration only refers to speeding up, but it includes any change in velocity, such as slowing down (deceleration) or changing direction.

Students might assume the origin must be the starting point of motion, rather than any chosen fixed reference point.

Students sometimes fail to specify the positive direction when dealing with vector quantities, leading to ambiguity in signs.

Students may incorrectly interpret the area under a velocity-time graph as total distance instead of displacement, especially when velocity is negative.