K326 / K327 / 2027
Kinematics overview

Lesson 2 of 6

Acceleration and slowing down

  • I can define uniform acceleration and calculate change in velocity / time.Syllabus

    Syllabus K326 / K327, 2(c). Define uniform acceleration and calculate change in velocity / time.

  • I can interpret examples of non-uniform acceleration.Syllabus

    Syllabus K326 / K327, 2(d). Interpret examples of non-uniform acceleration.

Make a guess. You are not marked.

A car is moving forwards. Its acceleration is -3 m/s2, with forwards taken as positive. What is the car doing?

  1. Moving backwards, because the acceleration points backwards.
  2. Stopped, because the acceleration is negative.
  3. Still moving forwards, but slowing down.
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Still moving forwards, but slowing down.

A negative acceleration means the velocity is decreasing by 3 m/s every second. The car keeps moving forwards until its velocity reaches zero.

Acceleration is the change in velocity per unit time.

Velocity includes direction. If that distinction is unfamiliar, review speed and velocity first.

Uniform acceleration means equal changes in velocity in equal time intervals. If velocity rises from 0 to 2 to 4 to 6 m/s at one-second intervals along a straight line, the acceleration is 2 m/s2. Every second adds another 2 m/s of velocity.

a = (v - u) / tu = initial velocity, v = final velocity, t = elapsed time. Acceleration a is measured in m/s2.

This gives the acceleration throughout an interval if it is uniform. If it varies, the calculation gives the average acceleration over that interval.

Worked example

Acceleration while slowing down

A trolley moving forwards slows uniformly from 8 m/s to 2 m/s in 3 s. Take forwards as positive.

a = (2 - 8) / 3 = -2 m/s2

The velocity decreases by 2 m/s each second. It still moves forwards throughout, because its velocity stays positive. We can also say it has a deceleration of 2 m/s2.

Try it step by step

Work it out in steps: Change in velocity v - u in m/s, then Acceleration (v - u) / t in m/s2.

  1. Problem 1. A car speeds up from 4 m/s to 16 m/s in 6 s. Find its acceleration.
  2. Problem 2. A train moving forwards slows from 25 m/s to 5 m/s in 8 s. Take forwards as positive. Find its acceleration.
  3. Problem 3. A motorcycle starts from rest and reaches 30 m/s in 12 s. Find its acceleration.
Show the answer

Problem 1.

Change in velocity v - u in m/s: v - u = 16 - 4 = 12 m/s

Acceleration (v - u) / t in m/s2: a = 12 / 6 = 2 m/s2

Problem 2.

Change in velocity v - u in m/s: v - u = 5 - 25 = -20 m/s

Acceleration (v - u) / t in m/s2: a = -20 / 8 = -2.5 m/s2 (the minus sign means it is slowing)

Problem 3.

Change in velocity v - u in m/s: v - u = 30 - 0 = 30 m/s

Acceleration (v - u) / t in m/s2: a = 30 / 12 = 2.5 m/s2

For non-uniform acceleration, the velocity changes by different amounts in equal times. A car leaving a junction may gain 2 m/s in its first second, then 3 m/s in the next, then only 1 m/s as the driver eases off. It speeds up in each interval, but not at a constant rate.

Constant speed along a straight line means zero acceleration. A fast car can have zero acceleration. A slower car gaining speed has non-zero acceleration.

Watch out for this

A student says: "A car with a negative acceleration must be moving backwards." What is wrong with this?

Show the answer

Negative acceleration means the acceleration points in the negative direction. A car moving forwards (positive velocity) with negative acceleration is slowing down. It moves backwards only if its velocity is negative.

Check your understanding

At 0, 1, 2 and 3 s, a car moving forwards has velocities of 0, 2, 5 and 9 m/s. Is its acceleration uniform?

  1. Not uniform: the velocity rises by 2, then 3, then 4 m/s.
  2. It is uniform, because its final velocity divided by the 3 s gives a steady 3 m/s2.
  3. Uniform: it is speeding up in the same direction throughout.
Show the answer

Not uniform: the velocity rises by 2, then 3, then 4 m/s.

The average accelerations in the three one-second intervals are 2, 3 and 4 m/s2. The acceleration is not constant.

Practise an exam question

Write your answer first, then tick the mark points it makes.

Exam-style question

Define acceleration. A car speeds up uniformly from 12 m/s to 30 m/s in 6.0 s. Calculate its acceleration. [3]

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