Solve each problem.
-The velocity of a particle (in $\mathrm{ft} / \mathrm{s}$ ) is given by $\mathrm{v}=\mathrm{t}^{2}-8 \mathrm{t}+3$, where $\mathrm{t}$ is the time (in seconds) for which it has traveled. Find the time at which the velocity is at a minimum.
A) $3 \mathrm{~s}$
B) $1.5 \mathrm{~s}$
C) $8 \mathrm{~s}$
D) $4 \mathrm{~s}$

Question

Quizplus · Accepted Answer

The velocity function $v(t) = t^2 - 8t + 3$ is a quadratic function, which has a minimum at the vertex. The vertex of a parabola $ax^2 + bx + c$ is at $t = -\frac{b}{2a}$. Here, $a = 1$ and $b = -8$, so the minimum velocity occurs at $t = \frac{8}{2} = 4$ seconds.

Solve Each Problem ft/s\mathrm{ft} / \mathrm{s}ft/s ) Is Given By v=t2−8t+3\mathrm{v}=\mathrm{t}^{2}-8 \mathrm{t}+3v=t2−8t+3

Solve Each Problem $\mathrm{ft} / \mathrm{s}$ ) Is Given By $\mathrm{v}=\mathrm{t}^{2}-8 \mathrm{t}+3$