Acceleration from velocity–time gradients

What you will learn

a = (v−u)/t; signed changes, gradients and tangents.

Specification mapping: B1.3.6

Prerequisites: B1.3.4

Physical principles

Acceleration is rate of change of velocity. Over an interval, average acceleration a = (v − u)/Δt. For constant acceleration this value applies throughout the interval. On a velocity–time graph the gradient gives acceleration; a tangent is required for instantaneous acceleration on a curve.

Choose one positive direction and use signed velocities. If velocity changes from −5 to −1 m s⁻¹, acceleration is positive even though motion remains negative: speed decreases. If velocity changes from −1 to −5 m s⁻¹, acceleration is negative and speed increases.

The units m s⁻² arise from (m s⁻¹)/s. A steep velocity–time gradient means large acceleration magnitude. A line of zero gradient means zero acceleration, which can occur at a non-zero velocity. Do not confuse a horizontal graph with an object being stationary unless the graph itself is at v = 0.

Scientific diagram and interpretation

Equations and relationships

a = (v−u)/t

Worked examples and applications

Common misconceptions

Negative acceleration means acceleration along the negative axis; whether speed rises or falls depends on velocity too.

Examination technique

Use the full velocity change, including signs, before dividing by elapsed time.

For an explanation, connect the physical cause to its effect. For a calculation, state the model, rearrange before substitution, retain intermediate digits, and finish with units. For a data question, refer to the actual readings and distinguish a trend from proof of a cause.

Check your understanding

Five questions. Choose an option, then Check Answer. Read the feedback and use Try Again to reset. Use Tab between controls, arrow keys within radio groups, and Enter or Space on buttons. These local practice answers are not saved.