📄 Cheat Sheets — Mechanics 1

Key facts, formulas and common mistakes for 1 of 1 chapters

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8 key facts·6 formulas·5 common mistakes·11 definitions·5 exam tips

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Definitions

scalar: A quantity which has only size, or magnitude.
vector: A quantity which has both magnitude and a direction in space.
distance: The total path length travelled by an object, irrespective of its direction.
position: The distance of an object above a fixed origin, including its direction.
displacement: The change in position of an object, measured from any position.
origin: A fixed reference point from which position is measured.
speed: A scalar quantity that describes how fast an object is moving, without regard to direction.
velocity: A vector quantity that describes the rate at which the position of an object changes, including its direction.
acceleration: A vector quantity that describes the rate at which the velocity of an object changes.
positive direction: The chosen direction in which quantities like position, displacement, and velocity are considered positive.
negative position: A position that is in the opposite direction to the defined positive direction, relative to the origin.

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Formulas

Ch 01

Average speed

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

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

Ch 01

Average velocity

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

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

Ch 01

Average acceleration

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

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

Ch 01

Area of a rectangle (under speed-time graph)

area = V T

Represents the distance travelled when speed is constant.

Ch 01

Area of a trapezium (under speed-time graph)

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

Represents the distance travelled when speed changes uniformly.

Ch 01

Area of a triangle (under speed-time graph)

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

Represents the distance travelled when speed increases uniformly from rest.

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Key Facts

Scalar quantities have magnitude only (e.g., distance, speed). Vector quantities have both magnitude and direction (e.g., displacement, velocity, acceleration).Ch 01
Displacement is the change in position (vector), while distance is the total path length travelled (scalar).Ch 01
Velocity is the rate of change of position (vector). Speed is the magnitude of velocity.Ch 01
Acceleration is the rate of change of velocity. A negative acceleration can mean slowing down in the positive direction, or speeding up in the negative direction.Ch 01
On a velocity-time graph, the gradient represents acceleration.Ch 01
On a velocity-time graph, the area between the graph and the time axis represents displacement.Ch 01
Average Velocity = Displacement / Time Taken.Ch 01
Average Speed = Total Distance Travelled / Total Time Taken.Ch 01

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Common Mistakes

✗Confusing distance with displacement, and speed with velocity. They are not interchangeable.Ch 01
✗Thinking negative velocity always means slowing down. It means the object is moving in the chosen negative direction.Ch 01
✗Believing acceleration only means speeding up. It is any change in velocity, including slowing down (deceleration).Ch 01
✗Calculating displacement from a velocity-time graph when the question asks for total distance. You must add the magnitudes of all areas for distance.Ch 01
✗Assuming the origin must be the starting point of motion. It is simply a fixed reference point.Ch 01

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Exam Tips

→Always define a positive direction at the start of a problem. This is crucial for getting the signs of displacement, velocity, and acceleration correct.Ch 01
→Sketch a velocity-time graph whenever possible. It helps visualize the motion and allows you to find acceleration (gradient) and displacement (area) easily.Ch 01
→Read the question carefully. If it asks for 'velocity', your answer needs a sign or direction. If it asks for 'speed', it's just the magnitude.Ch 01
→To find total distance from a velocity-time graph, add the absolute values of all areas (treat areas below the axis as positive).Ch 01
→For multi-stage journeys, remember that average speed is the *total* distance divided by the *total* time, not the average of the speeds.Ch 01

📄 Cheat Sheets — Mechanics 1

Mechanics 1 — Cheat Sheets

Definitions

Formulas

Key Facts

Common Mistakes

Exam Tips

📄 Cheat Sheets — Mechanics 1

Mechanics 1 — Cheat Sheets

Definitions

Formulas

Key Facts

Common Mistakes

Exam Tips