Answer
$28.1$ cm/s
Work Step by Step
Average velocity : $v_{avg}=\displaystyle \frac{\Delta x}{\Delta t}=\frac{x_{2}-x_{1}}{t_{2}-t_{1}}$
Instantaneous velocity: $v(t)=\displaystyle \frac{d}{dt}x(t)$
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$v(t)=\displaystyle \frac{d}{dt}x(t)= \displaystyle \frac{d}{dt}(9.75+1.50t^{3})$
$=3\cdot 1.50t^{2}=4.50t^{2}$ (cm/s)
At t=$2.50$,
$v(2.50)=4.50(2.50)^{2}$ cm/s$=28.1$ cm/s
