Use the position function $s ( t ) = 16 t ^ { 2 } + 109$ 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)16 feet/second
B)32 feet/second
C)0 feet/second
D)64 feet/second
E)limit does not exist

Question

Use the position function $s ( t ) = 16 t ^ { 2 } + 109$ 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)16 feet/second
B)32 feet/second
C)0 feet/second
D)64 feet/second
E)limit does not exist

Quizplus · Accepted Answer

The velocity at time $t = c$ is the derivative of the position function $s(t)$ with respect to $t$. Differentiating $s(t) = 16t^2 + 109$ gives $s'(t) = 32t$. Substituting $t = 2$ into $s'(t)$ gives $32(2) = 64$ feet/second.

Use the Position Function s(t)=16t2+109s ( t ) = 16 t ^ { 2 } + 109s(t)=16t2+109

Use the Position Function $s ( t ) = 16 t ^ { 2 } + 109$