Posted by **Leslie** on Thursday, November 8, 2012 at 9:55am.

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=i-3j with the velocity v=4i-3j. 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!

- Physics -
**drwls**, Thursday, November 8, 2012 at 11:14am
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.

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