Question

At time t equals or > 0, the acceleration of a particle moving on the x axis is a(t)=t+sint.? ...?

Answer 1

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