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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?

A

$t^{5}$

B

$t^{3}$

C

$t^{5/2}$

D

$t^{3/2}$

E

Not enough information

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