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).
I should only need those listed in the problem
The Attempt at a Solution
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.