Use the position function $s ( t ) = - 16 t ^ { 2 } + 120$ to find the velocity in feet/second at time $t = 2$ seconds. The velocity at time $t = c$ seconds is given by $\lim _ { t \rightarrow c } \frac { [ s ( c ) - s ( t ) ] } { ( c - t ) }$
A) limit does not exist
B) 32 feet/second
C) 64 feet/second
D) 0 feet/second
E) -64 feet/second

Question

Quizplus · Accepted Answer

The velocity at time $t = 2$ seconds is found by taking the derivative of the position function $s(t) = -16t^2 + 120$ with respect to $t$, which gives $v(t) = s'(t) = -32t$. Substituting $t = 2$ into $v(t)$ gives $v(2) = -32(2) = -64$ feet/second.

Use the Position Function s(t)=−16t2+120s ( t ) = - 16 t ^ { 2 } + 120s(t)=−16t2+120

Use the Position Function $s ( t ) = - 16 t ^ { 2 } + 120$