Question

The acceleration of an object is given by a(t)=cos(πt). The velocity of the object at time t=0 is 1/(2π). Which expression can be used to find the total distance traveled in the first 11/6 seconds?

Answer 1

D

Explanation:

v(t) = (1/pi) × sin(pi × t) + c

At t = 0, v = 1/2pi

1/2pi = 0 + c

v(t) = (1/pi)sin(pi×t) + 1/(2pi)

Takes a turn when v = 0

0 = (1/pi)sin(pi×t) - 1/(2pi)

sin(pi × t) = -½

pi × t = 7pi/6

t = 7/6

For t = 0 to t = 7/6,

V(t) > 0

So s(t) > 0

For t = 7/6 to t = 11/6,

Displacement is negative, so put a mod