The time-rate of change of displacement is?

Question

(a) acceleration
(b) distance
(c) velocity
(d) speed

Which is the answer? And why? What does it mean "time-rate of change"?

Answer 1

Hello James -

The time rate of change of displacement is how much the displacement changes over a certain amount of time (this is defined as velocity). Assuming that the rate is constant, this can be found by dividing the displacement by the time to get velocity. This value can be positive or negative. Speed, on the other hand, is simply the absolute value of the velocity, which is always positive.

The proper way to answer this question is with calculus, by taking the derivative of the equation that describes the displacement with respect to time - then evaluating the result at the time of interest. In this way, you do not have to assume that the velocity is constant.


Added: In other words, if the velocity is not constant you can still solve for it at any time. Note that velocity is negative if you are traveling in the negative x direction (where x is displacement). Hope this helps.