Which one of these is a unit of acceleration? Circle your answer. Is it metres per second cubed, kilometres per hour squared, kilometres squared per hour, or metres multiplied by seconds the power of negative one?
Let’s consider what we understand by the meaning of the word “acceleration.” It’s the rate at which the speed of an object changes. If a car accelerates, its speed is going to be increasing. And if it decelerates, its speed will be decreasing.
To be a little bit more strict in our definition, we can say that the acceleration is the change in speed of an object over a given period of time. And when we write this out, we write it as acceleration is equal to change in speed over time. This is the same as saying change in speed divided by time. And we’re going to use this definition to work out the units for acceleration.
Let’s begin by imagining we’re measuring in metres and seconds. The speed of our object would be metres per second. And that means that speed divided by time would be metres per second per second. This is exactly the same as saying metres per second squared.
Alternatively, we could measure speed in kilometres per hour. This time, acceleration would be speed divided by time, which is kilometres per hour per hour. Another way of saying this would be kilometres per hour squared. And the correct unit of acceleration in this example is kilometres per hour squared.
In fact, metres per second cubed and kilometres squared per hour are both nonsense units. The only one here that actually means anything aside from my unit of acceleration is metres multiplied by seconds the power of negative one. That’s another way of saying metres per second, which we have already seen is a unit of speed.