A ball is thrown straight down from the top of a 280-ft building with an initial velocity of -24 ft per second.The position function is .What is the velocity of the ball after 4 seconds?
A)The velocity after 4 seconds is -88 ft per second.
B)The velocity after 4 seconds is -104 ft per second.
C)The velocity after 4 seconds is -152 ft per second.
D)The velocity after 4 seconds is -40 ft per second.
E)The velocity after 4 seconds is -304 ft per second.

Question

A ball is thrown straight down from the top of a 280-ft building with an initial velocity of -24 ft per second.The position function is  .What is the velocity of the ball after 4 seconds? ​
A)The velocity after 4 seconds is -88 ft per second. 
B)The velocity after 4 seconds is -104 ft per second. 
C)The velocity after 4 seconds is -152 ft per second. 
D)The velocity after 4 seconds is -40 ft per second. 
E)The velocity after 4 seconds is -304 ft per second.

Quizplus · Accepted Answer

We know that the position function is s(t) = -16t^2 - 24t + 280 (using -24 ft per second as initial velocity).

So, to find the velocity after 4 seconds, we need to take the derivative of the position function with respect to time:

s'(t) = -32t - 24

Plug in t = 4:

s'(4) = -32(4) - 24 = -152

Therefore, the velocity of the ball after 4 seconds is -152 ft per second.

The best choice is C.

A Ball Is Thrown Straight Down from the Top of a 280-Ft