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
Mar 5, 2017

Answer:

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.