Use the position function $s ( t ) = 16 t ^ { 2 } - 102$ to find the velocity in feet/second at time $t = 2$ seconds.The velocity at time $t = c$ seconds is given by $\lim \frac { [ s ( c ) - s ( t ) ] } { ( c - t )_{c?t} }$ .
A)64 feet/second
B)limit does not exist
C)0 feet/second
D)32 feet/second
E)96 feet/second

Question

Use the position function $s ( t ) = 16 t ^ { 2 } - 102$ to find the velocity in feet/second at time $t = 2$ seconds.The velocity at time $t = c$ seconds is given by $\lim \frac { [ s ( c ) - s ( t ) ] } { ( c - t )_{c?t} }$ . 
A)64 feet/second
B)limit does not exist
C)0 feet/second
D)32 feet/second
E)96 feet/second

Quizplus · Accepted Answer

The velocity at time $t = 2$ seconds is found by taking the derivative of the position function $s(t) = 16t^2 - 102$ with respect to $t$, which gives $v(t) = \frac{d}{dt}(16t^2 - 102) = 32t$. Substituting $t = 2$ into $v(t)$ gives $v(2) = 32(2) = 64$ feet/second.

Use the Position Function s(t)=16t2−102s ( t ) = 16 t ^ { 2 } - 102s(t)=16t2−102

Use the Position Function $s ( t ) = 16 t ^ { 2 } - 102$