Moderate# Kinematics and Work

APPHMC-JBD3SV

The position function of a particle is given by $x(t) = k t^{5/2}$, where $k$ is a constant.

If the particle starts at rest and is propelled through some distance $d$ so that the trajectory matches $x(t)$, the work done on the particle is proportional to which power of t?