Question

Let s(t)=t^3+6t^2 be the position function of a particle moving along an axis, where s is in metres and t is in seconds. Find the the instantaneous acceleration a(t), and show the graph of acceleration with time.

Answer 1

The position function of a particle moving along an axis given by

$s(t)=t^3+6t^2$

Then velocity given by

$\begin{aligned} v(t) &=\frac{ds}{dt}\\ &= 3t^2+12t \end{aligned}$

Hence the acceleration given by

$\begin{aligned} a(t) &=\frac{dv}{dt}\\ &= 6t+12 \end{aligned}$

And the graph of acceleration