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=(d(t))/(t)`

Now,

`\begin{gathered} v=(2t^3)/(t) \\ v=2t^2 \end{gathered}`

At t = 0 sec.

`\begin{gathered} v=2t^2 \\ v=2*0 \\ v=0 \end{gathered}`

At t = 2 sec.

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

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