Solve the problem. -At time $t \geq 0$, the velocity of a body moving along the s-axis is $v = t ^ { 2 } - 10 t + 9$. When is the body's velocity increasing? A) t 5

Question

Solve the problem. -At time $t \geq 0$, the velocity of a body moving along the s-axis is $v = t ^ { 2 } - 10 t + 9$. When is the body's velocity increasing? A) t < 9 B) t < 5 C) t > 9 D) t > 5

Quizplus · Accepted Answer

To determine when the body's velocity is increasing, we need to find when its acceleration is positive. The acceleration of the body is given by the derivative of its velocity: $a=\frac{d}{dt}(t^2-10t+9)=2t-10$.
Setting this derivative to be positive gives us: 
$2t - 10 > 0$
$2t > 10$
$t > 5$
Therefore, the body's velocity is increasing for $t > 5$, or in other words, choice D.

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