Question

A particle moves in a straight line with an acceleration a ${ms}^{-2}$ at time $t$ seconds were $a=-\frac{1}{t^2}$. At time $t=1s$ the particle has a velocity of $3{ms}^{-1}$ then the velocity at $t=5s$ is $m\times {10}^{-2}m/s$ (where $m$ is an positive integer). Find $\frac{|m|}{5}$

Answer 1

$a=\frac{dv}{dt}=\frac{-1}{t^2}$

on integration

$v=\frac{1}{t}+c$

at t=1s $v=1+c=3$

c=2

at t=5s $v=\frac{1}{5}+2=\frac{11}{5}$m/s

$m=11$