Suppose a certain object moves in a straight line with velocity v(t)= -2+t+3sin(pi t) where v is in meters per second and t is in seconds. Determine the net change in distance of the object from time t=0 to time t=6 seconds and find the object's average velocity on this interval.

Question

Do I just find the antiderivative and solve when t=6? Please help

Answer 1

dx/dt = -2 + t + 3 sin (pi t)
pi t = 2 pi when t = 2 seconds
so we are doing several periods, danger, it luckily asks for the NET distance it goes and not the distance it travels during the 6 seconds (end - begin not total including back and forth)
so yes
x= -2t+t^2/2-(3/pi)cos(pi t)at 6 - at 0
danger again - remember cos 0 = 1

Answer 2

oh, and cos (6 pi) = 1 as well so forget about the trig :)

Answer 3

Thanks so much Damon!

Answer 4

You are welcome.