A particle has acceleration a=8e-2t m,s-2 for t 0 seconds, with v(0)=-1 m,s-1 and s(0)=4 m. Find its

Question

A particle has acceleration a=8e-2t m,s-2 for t 0 seconds, with v(0)=-1 m,s-1 and s(0)=4 m. Find its velocity and displacement functions.

Accepted Answer

$v=3-4\mathrm{e}^{-2t}\ \mathrm{m\,s^{-1}}$, $s=3t+2\mathrm{e}^{-2t}+2$ m.

Exponentially changing acceleration