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

kalpeshk2011

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..

LawrenceC

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.

kalpeshk2011

is the equation s=t⁴/4 + C??

LawrenceC

How about something like this

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"

LawrenceC

Your equation s=t^4/4 is incorrect because your previous integration was incorrect.

kalpeshk2011

But all this mathematics and integration in physics often confuses me. I don't know when to use which technique of integration. Moreover, I have only done the rudiments of calculus. Is there any definite way to know when to use which technique?

LawrenceC

You can use whichever you feel the most comfortable. If you had solved for the time you could use definite integrals and avoid constants of integration.

When you integrate x^n you get (x^(n+1))/(n+1). Does this help?

LawrenceC

And when you integrate

a*x^n you get a*(x^(n+1))/(n+1) where a is a constant. Do you see your mistake now?