Explanation:
Given: a = <em>-3v</em>^2
By definition, the acceleration is the time derivative of velocity <em>v</em><em>:</em>
<em>
</em>
Re-arranging the expression above, we get

Integrating this expression, we get


Since <em>v</em> = 10 when t = 0, that gives us k = -1/10. The expression for <em>v</em> can then be written as

or

We also know that

or

We can integrate this to get <em>s</em><em>:</em>

Let u = 30t +1
du = 30dt
so


So we can now write <em>s</em> as

We know that when t = 0, s = 8 m, therefore k = 8 m.

Next, we need to find the position and velocity at t = 3 s. At t = 3 s,


Note: velocity approaches zero as t --> 