A problem involving Force in terms of time?

[kalpeshk2011]

A problem involving Force in terms of time?

Homework Statement

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 traveled from t=0 when its velocity is 0 m/s?

Homework Equations

I think they should be F=ma , dv/dt = a, ds/dt = v

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?