# 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 ?

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 $p \left(t\right) = {t}^{2} - 2 t + 2$

Differentiating the expression,

$\frac{\mathrm{dp}}{\mathrm{dt}} = \frac{d}{\mathrm{dt}} \left[{t}^{2} - 2 t + 2\right]$

$p \left(t\right)$ denotes position and not momentum of the object. I clarified this because $\vec{p}$ symbolically denotes the momentum in most cases.

Now, by definition, $\frac{\mathrm{dp}}{\mathrm{dt}} = v \left(t\right)$ which is the velocity. [or in this case the speed because the vector components are not given].

Thus, $v \left(t\right) = 2 t - 2$

At $t = 1$

$v \left(1\right) = 2 \left(1\right) - 2 = 0$ units.