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.

Related questions
See all questions in Displacement and Velocity
Impact of this question
2096 views around the world
You can reuse this answer
Creative Commons License