Question

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!

Answer 1

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.