- #1

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## Homework Statement

A particle of mass m is subjected to a net force F(t) given by F(t)=F

_{0}(1-t/T)i; that is F(t) equals F

_{0}at t=0 and decreases linearly to zero in time T. The particle passes the origin x=0 with velocity v

_{0}i. Show that at the instant t=T and F(t) vanishes, the speed v and distance x traveled are given by v(T)=v

_{0}+a

_{0}T/2, and x(T)=v

_{0}T+a

_{0}T

^{2}/3, where a

_{0}=F

_{0}/m is the initial acceleration. Compare these results with Eqs (v

_{x}=v

_{0x}+a

_{x}t and x=x

_{0}+v

_{0x}t+1/2a

_{x}t

^{2}).

## Homework Equations

I should only need those listed in the problem

## The Attempt at a Solution

F=ma=F

_{0}(1-t/T)

F

_{0}=ma

_{0}

a=a

_{0}(1-t/T)

a=a

_{0}-a

_{0}t/T

v=v

_{0}+at

v=v

_{0}+(a

_{0}-a

_{0}t/T)t

When t=T, those a

_{0}'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.