Question

The distance traveled, in feet, of a ball dropped from a tall building is modeled by the equation d(t) = 16t2 where d equals the distance traveled at time t seconds and t equals the time in seconds. What does the average rate of change of d(t) from t = 2 to t = 5 represent?
A. The ball travels an average distance of 112 feet from 2 seconds to 5 seconds.

B. The ball falls down with an average speed of 48 feet per second from 2 seconds to 5 seconds.

C. The ball falls down with an average speed of 112 feet per second from 2 seconds to 5 seconds.

D. The ball travels an average distance of 48 feet from 2 seconds to 5 seconds.

Answer 1

When  t=2, the ball has fallen     d(2) = 16 (2²) = 64 feet .

When  t=5, the ball has fallen     d(5) = 16 (5²) = 400 feet .

Distance fallen from  t=2  until  t=5  is  (400 - 64) = 336 feet.

Time period between  t=2  until  t=5  is  (5 - 2) = 3 seconds.

Average speed of the ball from  t=2  until  t=5  is

                 (distance covered) / (time to cover the distance)

             =            336 feet        /        3 seconds       =  112 feet per second.

That's what choice-C says.