Acceleration: Change in velocity

Have you noticed something? When you stand on a bus, and the bus is going straight ahead, at constant speed, then it's no problem at all to keep your balance... It's only when the bus brakes... ... speeds up... ... or makes a turn... ...

that you'll sway, and have to hold on. When something changes velocity, it is accelerating. Check this out! This bus is standing still. And now it starts driving.

The driver gently presses the accelerator, and drives straight ahead. When the bus has been driving for six seconds, the velocity has increased from zero to... let's say twelve metres per second. Since the velocity has changed, we say that the bus is accelerating. Acceleration is: how fast the velocity is changing -- the rate of change in velocity.

How much does the bus accelerate? That is, at what rate does the velocity of the bus change? Well, here's the velocity going from zero to twelve metres per second. The change in velocity is then: from zero to twelve -- that's an increase of twelve metres per second. And to get the rate of change, we need the time too.

Time goes from zero to six seconds. So, we divide: change in velocity by time, and get... the rate of change: the acceleration. 12 divided by six is two. But, what units do we use?

Metres per second, divided by seconds? That makes two divisions... Metres per second... per second? Yes, that is actually the unit for acceleration: metres per second, per second!

But we usually write it like this: Metres per second-squared. Acceleration is the rate of change in velocity, and it's measured in metres per second-squared. There, the bus was driving straight ahead and changed its velocity at a constant rate. But acceleration can actually mean other things than increase in velocity. If the driver brakes for example, an acceleration.

that too, is a change in velocity: In daily life, we talk about acceleration as an increase in velocity. But in physics, acceleration is any change in velocity. So, when the bus slows down, from 12 metres per second to... say half that velocity... ... then we have a change in velocity of minus six metres per second.

And, if that change took three seconds, then the acceleration was: Minus six metres per second... ... divided by three seconds. Which equals minus two metres per second-squared. Negative acceleration, that's when the velocity decreases. Sometimes you may hear deceleration or retardation instead of acceleration.

But we stick to negative acceleration. When a bus is speeding up or slowing down, you need to hold on, to keep from falling. At an even velocity, when the bus is not accelerating, you can stand steadily. If you suddenly need to hold on, when standing on a bus, the velocity has changed. The greater the rate of change, the harder you need to hold on.

If you measure the rate of change, you do that in metres per second-squared. And you have measured acceleration.