Question

If the velocity of a car traveling in a straight line at time v(t) then the difference in its odometer readings between time t=a and t=b is

A. integral a to b of the absolute value of v(t)dt
B. integral a to b of v(t)dt
C. the net displacement of the car's position from t =a to t =b
D. the change in the car's position from t = a to t = b
E. none of these

Answer 1

B. integral a to b of v(t) dt.

Explanation:

The difference in the odometer reading of car travelling in a straight line between two instants is:

`v(t) = (ds)/(dt)`

`ds = v(t)\,dt`

`s_(B) - s_(A) = \int\limits^{t_(b)}_{t_(a)} {v(t)} \, dt`

Hence, the right answer is B.