# Calculating velocity and position from time variating force

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1. Sep 9, 2015

### jeremyskate

1. The problem statement, all variables and given/known data

2. Relevant equations

v(t)=∫a(t)dt
r(t)=∫v(t)dt
3. The attempt at a solution
f=ma
a(t)=f/m
a(t)=(4/5t^2i-3/5tj)
(integrate)
v(t)=4/5i(t^3/3+c1)-3/5j(t^2/2+c2)
how can i get rid of the c1 c2?

2. Sep 9, 2015

### andrewkirk

You use initial conditions to get rid of them.
One condition is that initial position is the origin.
Another initial condition is the initial velocity, which is not stated, but needs to be. Since they haven't stated it, the simplest approach is to assume it is zero.

3. Sep 9, 2015

### jeremyskate

v(0)=0 would make the most sense but since it isn't mentioned I also thought of leaving the constants and integrating them as well to get the position function, but the end result would have way too much undefined variables...

4. Sep 9, 2015

### andrewkirk

If you assume that the initial velocity is $v_1\mathbf{i}+v_2\mathbf{j}$ then you will get rid of c1 and c2 and instead have $v_1,v_2$ in all your answers. That shouldn't be too onerous.

5. Sep 10, 2015

erroneous?