Below is the solution:
The integral of acceleration yields velocity, which we are trying to find.
So int(a(t)) = (t^2)/2 - cos(t) + C.
So we can also say that v(t) = (t^2)/2 - cos(t) + C.
*The constant, C, is very important in this case. We need to find when v(t) = 0. We can not do that without first knowing C.
2. Solve for C.
-2 = v(0).
-2 = (t^2)/2 - cos(t) + C.
-2 = -cos(t) + C.
-2 = -1 + C
-1 = C.
Now we have the full velocity equation.
v(t) = (t^2)/2 - cos(t) - 1.
4. Solve for t when velocity is 0.
0 = (t^2)/2 - cos(t) - 1.
t = 1.478 or -1.478
*time cannot be negative, so answer is b.1.48