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

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