A particle moves along the $x$-axis so that its position at time $t$ is given by $x(t)=t^2-8t+7$. For what value of $t$ is the velocity of the particle zero?

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Start by taking the derivative with respect to time. This will give us the velocity equation.

$$x(t)=t^2-8t+7$$ $$v(t)=2t-8$$

Set it equal to 0:

$$0 = 2t-8$$ $$t=\boxed{4}$$