Question

The distance d (in inches) that a beetle travels over time + (inseconds) is given by the function d (t) = 2t^3 . Find the averagespeed of the beetle from t1 = 0 second to t2 = 2 seconds.inches/second

Answer 1

Given distance,

$d(t)=2t^3$

Let v is the speed of the beetle.

It is given by

$v=\frac{d(t)}{t}$

Now,

$\begin{gathered} v=\frac{2t^3}{t} \\ v=2t^2 \end{gathered}$

At t = 0 sec.

$\begin{gathered} v=2t^2 \\ v=2\times0 \\ v=0 \end{gathered}$

At t = 2 sec.

$\begin{gathered} v=2t^2 \\ v=2\times2^2 \\ v=8\text{ m/sec} \end{gathered}$

So, the average speed of the beetle is 8 m/sec.