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 = 4 secs?

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 = 4 secs?

 7.67 

−3.33 

−5.33 

3.33

Answer 1

Remember that velocity is the derivative of displacement with respect to time. v=dx/dt

In this case, we have the velocity but need to know the displacement.

We integrate the velocity function with the bounds of t=0 to t=4 s

∫ -t² + 4 dt with integral bounds t=0 and t=4. Calculate this definite integral and you should get the answer.

Answer 2