Solve the problem.
-An explosion causes debris to rise vertically with an initial velocity of 96 feet per second. The function $$s ( t ) = - 16 t ^ { 2 } + 96 t$$ describes the height of the debris above the ground, s(t), in feet, t seconds after the explosion. What is the instantaneous speed of the debris 4.8 second(s) after the explosion?
A) 153.6 ft/sec
B) -57.6 ft/sec
C) 57.6 ft/sec
D) -153.6 ft/sec

Question

Quizplus · Accepted Answer

The instantaneous speed of the debris at any time $t$ is given by the derivative of the function $s(t)$ with respect to $t$, which represents the velocity of the debris. The derivative of $s(t) = -16t^2 + 96t$ is $s'(t) = -32t + 96$. Substituting $t = 4.8$ seconds into $s'(t)$ gives $s'(4.8) = -32(4.8) + 96 = -153.6 + 96 = -57.6$ ft/sec.

Solve the Problem s(t)=−16t2+96ts ( t ) = - 16 t ^ { 2 } + 96 ts(t)=−16t2+96t

Solve the Problem $s ( t ) = - 16 t ^ { 2 } + 96 t$