Q.A particle moves along a straight line so that the distance covered in $t$ seconds is $s(t)=4t^2-3t+5$ metres. Find

For a quantity that changes with time -- most

concretely, the distance $s(t)$ covered by a moving particle -- the average rate of change over

an interval $[t,t+\Delta t]$ is $\Delta s/\Delta t$, the change in the quantity divided by the

change in time; letting $\Delta t$ shrink to zero turns this average into the instantaneous rate

of change (instantaneous velocity) at the single instant $t$, defined as the limit

$\lim_{\Delta t\to0}[s(t+\Delta t)-s(t)]/\Delta t$. Nothing in this argument is specific to

distance: for any function $y=f(x)$ of any variable $x$, the identical limiting process defines

the derivative of $f$ at $x$ as the instantaneous rate of change of $y$ with respect to $x$, …