Simple math problem in one dimension

  • Thread starter Slusho
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  • #1
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Homework Statement


A particle of mass m is subjected to a net force F(t) given by F(t)=F0(1-t/T)i; that is F(t) equals F0 at t=0 and decreases linearly to zero in time T. The particle passes the origin x=0 with velocity v0i. Show that at the instant t=T and F(t) vanishes, the speed v and distance x traveled are given by v(T)=v0+a0T/2, and x(T)=v0T+a0T2/3, where a0=F0/m is the initial acceleration. Compare these results with Eqs (vx=v0x+axt and x=x0+v0xt+1/2axt2).


Homework Equations


I should only need those listed in the problem


The Attempt at a Solution


F=ma=F0(1-t/T)
F0=ma0
a=a0(1-t/T)
a=a0-a0t/T

v=v0+at
v=v0+(a0-a0t/T)t

When t=T, those a0's cancel each other out and you end up with zero. I've also tried starting with the other one, and taking derivatives, to no avail. I can't get the math to work out to give me those coefficients.

Help is GREATLY appreciated.

Homework Statement





Homework Equations





The Attempt at a Solution

 

Answers and Replies

  • #2
43
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So you've already written Newton's 2nd Law, that's important. But what are the time derivative relationships between acceleration, velocity, and position? Use those relationships to work backwards from Newton's 2nd Law to obtain v(t) and x(t).
 

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