(a) displacement, instantaneous speed, average speed, velocity and…

The idea

Kinematics distinguishes five quantities. Displacement is the straight-line distance in a stated direction from start to finish, so it is a vector and can be zero after a round trip. Instantaneous speed is the magnitude of velocity at one instant, found from the gradient of a distance–time graph or a tangent. Average speed is total distance divided by total time, a scalar. Velocity is displacement divided by time, a vector, so direction matters. Acceleration is the rate of change of velocity, a vector, and occurs whenever speed, direction or both change.

For example: A car returning to its start has zero displacement but non-zero average speed.

What earns the marks

• Displacement is the straight-line distance from start to finish in a stated direction.
• Instantaneous speed is the magnitude of velocity at a particular instant.
• Average speed is total distance travelled divided by total time taken.
• Velocity is displacement divided by time and is a vector.
• Acceleration is the rate of change of velocity, so a change of direction also produces acceleration.

Common mistakes and how to put them right

• Treating distance and displacement as interchangeable.

  Put it right: Displacement includes direction and can be zero for a closed loop.

• Confusing average speed with instantaneous speed.

  Put it right: Average speed uses total distance and total time.

• Assuming constant speed means zero acceleration.

  Put it right: Changing direction at constant speed still gives acceleration.

Exam tips

• Write the defining equation and substitute values with units before choosing an option.
• Check whether the quantity is a vector or scalar before comparing magnitudes.
• For round trips, separate total distance from displacement.