Find the displacement

Question

For an object whose velocity in ft/sec is given by v(t) = -t² + 4, what is its displacement, in feet, on the interval t = 0 to t = 3 secs?

Question options:

1)	7.67
2)	-3.00
3)	-0.33
4)	3.00

Answer 1

velocity is the derivative of position with respect to time, so position is the integral of velocity with respect to time.

so our formula is the integral from 0 to 3 of (-t² + 4)dt

The integral of (-t² + 4)dt is -t³/3 + 4t

Plugging in t = 3, we get -27/3 + 12 = -9 + 12 = 3

plugging in t = 0, we get 0.

3-0 = 3 feet