For an object whose velocity in ft/sec is given by v(t) = −t^2+ 6, what is its displacement, in feet, on the interval t = 0 to t = 3 secs?

9 ft

Explanation: Since the velocity is the derivative of position vector and the displacement is the difference between two position vectors, the displacement is computed as a definite integral of velocity for a time interval (from one time to another time). 

Because the time interval is t =0 second to t = 3 seconds, the displacement is calculated as



Hence, the displacement is 9 ft.