Solve the problem.
-The position of a body moving on a coordinate line is given by $\mathrm { s } = \mathrm { t } ^ { 2 } - 7 \mathrm { t } + 4$, with $\mathrm { s }$ in meters and $\mathrm { t }$ in seconds. When, if ever, during the interval $0 \leq t \leq 7$ does the body change direction?
A) t = 7 sec
B) t = 14 sec
C) t = 3.5 sec
D) no change in direction

Question

Quizplus · Accepted Answer

To determine when the body changes direction, we need to find when the velocity, which is the derivative of the position function $s(t) = t^2 - 7t + 4$, equals zero. The velocity is $v(t) = s'(t) = 2t - 7$. Setting $v(t) = 0$ gives $2t - 7 = 0$, which solves to $t = 3.5$ seconds. This is within the given interval $0 \leq t \leq 7$, indicating a change in direction at $t = 3.5$ seconds.

Solve the Problem s=t2−7t+4\mathrm { s } = \mathrm { t } ^ { 2 } - 7 \mathrm { t } + 4s=t2−7t+4

Solve the Problem $\mathrm { s } = \mathrm { t } ^ { 2 } - 7 \mathrm { t } + 4$