What does negative acceleration mean?

Question

An object moving in a straight line has an acceleration of -2 m/s². Is the object speeding up, slowing down, or is more information needed? Give a complete explanation with examples.

Answer 1

The answer is "more information is needed."

Don't be disheartened if you got it wrong... most students do the first time.

An acceleration of -2 m/s², which can be written as -2m/s/s; that is -2 meters per second, per second. It is the rate of change of velocity. An acceleration of -2 m/s/s means that each second, the velocity changes by -2 m/s.

Example Slowing Down

Suppose the velocity of the object is 10 m/s. That means that each second, the velocity will be 8 m/s, 6 m/s, 4 m/s. The object is slowing down (the magnitude of the velocity is decreasing) because the velocity is positive and the change in velocity is negative.

Example Speeding Up

Now, suppose that the velocity is instead -5 m/s. That means that each second, the velocity will be -7 m/s, -9 m/s, -11 m/s, etc. The object is speeding up (the natnitude of the velocity is increasing) because the velocity is negative and the change velocity is also negative.

Therefore the rule of thumb is as follows: if acceleration and velocity have the same sign, the speed increases. If their signs are opposite, the speed decreases.

Answer 2

Roger's answer is perfect !