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A problem involving Force in terms of time? 
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#1
Mar212, 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/s^{2}t^{2} 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=6t^{2} So by newton's second law, F=3(2t^{2})=ma so i got a = 2t^{2} Integrating this, i got v=t^{3}+C and s=t^{4}/4 Now i thought initial velocity will be 10m/s which i put in C and V=0 so, 0 = t^{3}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.. 


#2
Mar212, 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. 


#3
Mar212, 10:06 AM

P: 6

is the equation s=t^{4}/4 + C??



#4
Mar212, 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" 


#5
Mar212, 10:34 AM

P: 1,195

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



#6
Mar212, 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?



#7
Mar212, 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? 


#8
Mar212, 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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