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 ?

1 Answer
Dwight
Mar 5, 2017

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.

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