Recall that the acceleration a(t) of a particle moving along a straight line is the instantaneous rate of change of the velocity v(t); that is,

a(t) = d/dt v(t)

Assume that a(t) = 32 ft/s². Express the cumulative change in velocity during the interval [0, t] as a definite integral, and compute the integral.

So far I got:

v(t) - v(0) = the integral from 0 to t of a(u)du, but im not sure where to go from there.

Thank you so much for your help!!

1 answer

That is correct.

a(u) = 32

v(u) = 32u + Vo

v(t) - v(0) = 32t