Ian tosses a bone up in the air for his dog, Spot. The height, h, in feet, that Spot is above the ground at the time t seconds after she jumps for the bone can be represented by the function h (t) = -16t+20t. What is Spot's average rate of ascent, in feet per second, from the time she jumps into the air to the time she catches the bone at t=1/2 seconds

Hence the rate of ascent at t=1/2 is 12 ft/sec

Step-by-step explanation:

Given:

Height function as h (t) = -16t^2+20t

To find:

Velocity at t=1/2. i. e. Average rate of ascent

Solution:

Average rate is given by

V=f (t) - f (a) / (t-a)

now here t=1/2 and a=0

Hence Equation becomes

V=f (1/2) - f (0) / (1/2-0)

So at t=1/2

f (1/2) = -16 (1/2) ^2+20 (1/2)

=-4+10

=6 fts

Now, t=0

f (0) = 16 (0) ^2+20 (0)

=0 ft

Hence V=f (1/2) - f (0) / (1/2-0)

V = (6-0) / (1/2-0)

V=6*2

V=12 ft/sec