METRONMETHOD. REASON. LEARN.
Motion · 12 min

Acceleration

Speeding up, slowing down and changing direction all involve acceleration. It describes how motion changes, not simply how fast something moves.

01Why this matters

Speeding up, slowing down and changing direction all involve acceleration. It describes how motion changes, not simply how fast something moves.

02See it

time (s)0410velocity (m/s)2
Velocity rises from 2 to 10 m/s over four seconds. The gradient is 2 m/s².
2 m/s initially+8 m/s change4 s elapsed2 m/s²
Read left to right: 2 m/s initially → +8 m/s change → 4 s elapsed → 2 m/s². Each panel connects one part of the example.

03Understand it

Acceleration is the rate of change of velocity with time.

Average acceleration is final velocity minus initial velocity, divided by elapsed time. Its SI unit is m/s²: a change in metres per second each second. Choose a positive direction before using signed velocities. Negative acceleration does not always mean slowing down; it means the acceleration points in the negative direction.

04Guided example

A trolley’s velocity changes from 2 m/s to 10 m/s in 4 s along a straight line.

  1. Find the velocity change: 10 − 2 = 8 m/s.
  2. Divide by elapsed time: 8/4 = 2 m/s².
  3. If acceleration is constant, the velocity increases by 2 m/s in each second.

05Try it

Velocity changes from 0 to 12 m/s in 3 s. Average acceleration?
A little hint

Find change in velocity, then divide.

06Practise it

Velocity changes from 10 to 4 m/s in 2 s. Acceleration?
A little hint

Keep the sign of the velocity change.

Start at 3 m/s and accelerate at 2 m/s² for 4 s. Final velocity?
A little hint

Use v = u + at.

07Use it in the real world

A train slowing from 20 m/s to 8 m/s in 6 s has average acceleration (8 − 20)/6 = −2 m/s² with forward chosen positive.

Go a little deeper

A car moving at constant speed around a curve accelerates because its velocity direction changes. This cannot be represented by a change in speed alone.

08Quick check

Constant velocity 8 m/s for 5 s. Acceleration?
A little hint

Has velocity changed?

09Summary

Acceleration is the rate of change of velocity with time. If acceleration is constant, the velocity increases by 2 m/s in each second.

Before moving on, explain the worked example in your own words. Use the hint on any question you want to revisit.

10Key idea

a = (v − u)/t

a: acceleration in m/s²; u: initial velocity and v: final velocity in m/s; t: elapsed seconds.

v = u + at, for constant acceleration

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