Question

if the displacement of the particle is given as x=1/3t^6+1/6t^3-2/5t^-5. Find the velociry.

Answer 1

$v=\frac{dx}{dt}\\ =\frac{d}{dt}\left(\frac{1}{3}t^6+\frac{1}{6}t^3-\frac{2}{5}t^{-5}\right)\\ =\frac{1}{3}\cdot6t^5+\frac{1}{6}\cdot3t^2-\frac{2}{5}(-5t^{-6})\\ =2t^5+\frac{1}{2}t^2+2t^{-6}$