The position of an object moving along a line is given by #p(t) = t^2 - 2t +2#. What is the speed of the object at #t = 1 #?

1 Answer
Aritra G.
Jun 4, 2016

Velocity of an object is the time derivative of it's position coordinate(s). If the position is given as a function of time, first we must find the time derivative to find the velocity function.

Explanation:

We have #p(t) = t^2 - 2t + 2#

Differentiating the expression,

#(dp)/dt = d/dt [t^2 - 2t + 2] #

#p(t)# denotes position and not momentum of the object. I clarified this because #vec p# symbolically denotes the momentum in most cases.

Now, by definition, #(dp)/dt = v(t)# which is the velocity. [or in this case the speed because the vector components are not given].

Thus, #v(t) = 2t - 2#

At #t = 1#

#v(1) = 2(1) - 2 = 0# units.

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