Acceleration — Cambridge IGCSE Co-ordinated Sciences 0654 - Physics Revision Notes & Topical Questions

Acceleration is the rate at which velocity changes. An object accelerates when it speeds up, slows down or changes direction. It is a vector: it has size and direction. In this topic we mainly consider straight-line motion, where the direction is either forwards or backwards.

a = (v − u) ÷ t

Here a is the acceleration in metres per second squared (m/s²), v is the final velocity (m/s), u is the initial velocity (m/s) and t is the time taken for the change (s). The quantity (v − u) is the change in velocity, Δv.

The unit m/s² means

• how many metres per second the velocity changes by each second.
• An acceleration of 3 m/s² means that the velocity increases by 3 m/s every second.

If the final velocity is greater than the initial velocity, then (v − u) is positive and the acceleration is positive. If the object slows down, (v − u) is negative, and the acceleration is negative. A negative acceleration is also called deceleration or retardation. The sign shows the direction of the acceleration relative to the direction chosen as positive.

For example, a car moving at 20 m/s that brakes to rest in 5.0 s has a = (0 − 20) ÷ 5.0 = −4.0 m/s². Its speed falls by 4.0 m/s every second.

Zero acceleration means constant velocity. A car moving at a steady 30 m/s on a straight road has zero acceleration even though it is moving fast. And a car going round a bend at constant speed is accelerating because its direction, so its velocity, is changing.

When an object falls and air resistance can be ignored, it accelerates downwards at a rate that is the same for all objects close to the Earth's surface: g = 9.8 m/s². Each second a falling object's speed increases by 9.8 m/s. After 1.0 s it moves at 9.8 m/s, after 2.0 s at 19.6 m/s, and so on.

In real situations, air resistance increases with speed, and so the acceleration decreases until the object reaches a steady terminal velocity. A feather falls more slowly than a coin because of air resistance, but in a vacuum both fall with the same acceleration.

If an object is thrown upwards, it decelerates at 9.8 m/s² while rising, stops momentarily at the top, then accelerates downwards at 9.8 m/s². The acceleration is downwards all the time, even at the top.

On a velocity-time graph, acceleration is the gradient of the line (1.1.5). Also, Newton's second law relates acceleration to the resultant force and the mass: F = m a, so a bigger resultant force gives a bigger acceleration for the same mass. The equation for acceleration also leads to the equations of uniform acceleration in 1.1.7.

Typical accelerations help us judge whether an answer is realistic.

An important idea is that acceleration depends on how quickly the velocity changes, not on how big the velocity is.