Question

The position of an object moving along a line is given by `p(t) = t^2 - 6t +3`. What is the speed of the object at `t = 3`?

Answer 1

As the speed is the derivative of the position function, at `t=3`, its speed is zero.

Explanation:

I have to assume you are working with calculus in this Physics course. The first derivative of the position with respect to time will give the velocity function:

`(dp(t))/(dt) = v(t)`

`d/(dt)(t^2-6t+3) = 2t-6`

If we evaluate this function at `t=3`

`v=2(3)-6 = 0`

The object has (momentarily) stopped at `t=3` s. (But note that this does not imply the position or the acceleration is zero. In fact it's position is `3^2-6(3)+3=-6`

And, for the record, its acceleration is the second derivative of `p(t)` or the first derivative of `v(t)`, namely 2.