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A problem involving Force in terms of time?

by kalpeshk2011
Tags: force, newton's laws, physics, velocity
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kalpeshk2011
#1
Mar2-12, 09:41 AM
P: 6
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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LawrenceC
#2
Mar2-12, 10:04 AM
P: 1,195
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
#3
Mar2-12, 10:06 AM
P: 6
is the equation s=t4/4 + C??

LawrenceC
#4
Mar2-12, 10:31 AM
P: 1,195
A problem involving Force in terms of time?

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
#5
Mar2-12, 10:34 AM
P: 1,195
Your equation s=t^4/4 is incorrect because your previous integration was incorrect.
kalpeshk2011
#6
Mar2-12, 10:36 AM
P: 6
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
#7
Mar2-12, 10:39 AM
P: 1,195
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
#8
Mar2-12, 10:53 AM
P: 1,195
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?


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