Question

Hi i have homework can you help me

Answer 1

Explanation:

The particle will be at rest when its velocity $v(t)$ is equal to zero. Recall that the velocity is simply the derivative of the position $x(t)$ with respect to time:

$v(t) = \dfrac{dx}{dt}$

Since $x(t) = t^2 - 2t + 2$

then

$v(t) = \dfrac{d}{dt}(t^2 - 2t + 2) = 2t - 2 = 0$

Solving for t, we find that the particle will be at rest at

$t = 1\:\text{s}$