Acceleration

Acceleration — the rate of change of velocity:

acceleration = change in velocity ÷ time taken

or a = (v − u) / t, where u is the initial velocity, v the final velocity, both in m/s, and t in seconds. Acceleration is measured in m/s².

Deceleration is negative acceleration. There is no separate equation. An object slowing from 20 m/s to 5 m/s in 3 s has an acceleration of (5 − 20) ÷ 3 = −5 m/s². The minus sign is the physics, not a mistake.

Velocity–time graphs put velocity on the vertical axis and time on the horizontal. They carry two separate pieces of information, and confusing them is the most common error in this topic:

• The gradient is the acceleration.
• The area under the graph is the distance travelled.

A horizontal line here does not mean stationary — it means constant velocity. The object is moving steadily. It is stationary only where the line sits on the time axis at zero.

Finding the area — split the shape into rectangles and triangles. The area of a triangle is ½ × base × height, and for a rectangle it is base × height. Add them up.

The third equation of motion appears on the 4PH1 specification and is worth recognising:

v² = u² + 2 a s

It is the one to reach for when the time is not given and not asked for.

Example: a car accelerates from rest at 2 m/s² over 50 m. Using v² = u² + 2as gives v² = 0 + 2 × 2 × 50 = 200, so v = 14 m/s. Getting there with a = (v−u)/t would have meant finding the time first.

A common trap: an object can be accelerating while its speed is constant, if its direction is changing. Acceleration is a change in velocity, and velocity includes direction.