## A problem involving Force in terms of time????

1. The problem statement, all variables and given/known data
There is a body of 3 kg which is moving to the right with a velocity of 10 m/s. A force of 6 N/s2t2 is applied on the body to the left. How much distane will the body have travelled from t=0 when its velocity is 0 m/s?

2. Relevant equations
I think they should be F=ma , dv/dt = a, ds/dt = v

3. The attempt at a solution
F=6t2
So by newton's second law,
F=3(2t2)=ma
so i got a = 2t2
Integrating this, i got v=t3+C and s=t4/4
Now i thought initial velocity will be -10m/s which i put in C
and V=0
so, 0 = t3-10 or t=2.31 seconds
I have no clue what to do after this. I thought i'll substitute the value of t in the equation with s in it, but some how i don't think its correct. And i don't have any answers to check my solution. please help..

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 Hint: Equation for s has to be written in a different form. With constant acceleration it is s = V0t+.5at^2 You do not have constant acceleration.
 is the equation s=t4/4 + C??

## A problem involving Force in terms of time????

s = V0 * t + integral(a(t) * t)*dt

where a(t) is the acceleration, F(t)/m.

You have a mistake below for your time

"Integrating this, i got v=t^3"