Question

A particle moves along the x-axis obeying the equation $x=t(t-1)(t-2)$, where $x$ is in meter and $t$ is in second. Find the initial velocity of the particle ($m/s$)

Answer 1

Given equation of path of particle is $x=t(t-1)(t-2)=t^3-3t^2+2t$

Now,

$v=\frac{dx}{dt}=3t^2-6t+2$.

And initial velocity is the velocity of particle at time $t=0$. Hence ;

$v_i=3(0{)}^2-6(0)+2=2m{s}^{-1}$