Physics
posted by Leslie .
A particle moves with the acceleration a=2e(^t)i+5cos(t)j
In the instant when t=0 the particle is at the point r=i3j with the velocity v=4i3j. Calculate the velocity and position of the particle at any instant.
I tried doing the problem and ended up just rearranging the formulas and meshing them together, which I know isn't correct. I would really appreciate a walkthrough of how to do this type of problem. Thank you!

At t = 0, x = 1 and y = 3
At t = 0, Vx = 4 and Vy = 3
At all times, ax =2 e^t and
ay = 5 cos(t)
Solve by integration.
Vx = 2 e^t + C
C = 6
Vy = 5 sin(t) + C'
C = 3
Vx = 2 e^t +6
Vy = 5 sin(t) 3
(The constants were obtained from the values of Vx and Vy at t = 0)
Now integrate Vx(t) and Vy(t) and apply the initial x and y conditions at t =0, to get the solutions for x and y at any time t.