When travelling on a KCR train, we notice that the train does not move at a constant velocity between two stations. It speeds up when it has just departed from one station, and it slows down when it is about to arrive at another station. These changes in velocity can be described by acceleration, which is defined as the rate of change of velocity with time:

Fig. 4-1 Braking a car involves acceleration with a change in speed only (deceleration is regarded as a negative acceleration).

Fig. 4-2 A bicycle undergoes acceleration with a change in direction only.

Fig. 4-3 A roller coaster undergoes acceleration with changes in both speed and direction.

The SI unit for acceleration is metre per second squared (). For example, when an object is moving with an acceleration of , its velocity increases by 1 every second.

If the acceleration of an object is a constant and nonzero, we say that the object is in a uniformly accelerated motion. The constant acceleration a, the initial velocity u, the final velocity v, and the travelling time t are then related by

Since velocity is a vector quantity which has both magnitude and direction, acceleration is also a vector quantity. Thus a change in velocity may involve a change in speed and/or the direction of motion. Take braking a car as an example (Fig. 4-1). When a driver notices that a traffic light turns red, he applies the brake to stop the car. The speed of the car decreases to zero, but the direction of motion remains unchanged. Thus braking a car involves an acceleration with a change in speed only. A bicycle travelling at a constant speed around a circular stadium also has an acceleration (Fig. 4-2). In this case the speed is a constant but the direction of motion is changing. A roller coaster moving up and down on the railway undergoes acceleration with changes in both speed and direction (Fig. 4-3).