Calculus 1 - Average Velocity Exam Practice Help

Question

A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 28 ft/s. Its height in feet after t seconds is given by .

Find the average velocity for the time period beginning when t=1 and lasting

.01 s:

.005 s:

.002 s:

.001 s:

I was able to get the first answer which is -12.2, but I can't seem to figure out the rest.

Answer 1

When finding an average velocity, you are getting a slope of two points. Beginning at t=1 and lasting 0.01 s means that the ending time t is 1+0.01= 1.01 s. So you input these two time t= 1 and 1.01 to get the Y values. Therefore the two points are beginning at (1, 8) and ending at (1.01, 7.878). The average velocity is (y2-y1)/(t2-t1), that is (7.878-8)/(1.01-1) = -12.2 ft/s.

By using the same logic,

.005 s: (7.9395-8)/(1.005-1)= -12.1 ft/s

.002 s: (7.97592-8)/(1.002-1)= -12.04 ft/s

.001 s: (7.98798-8)/(1.001-1)= -12.02 ft/s

As lasting time is getting longer the average velocity is getting faster downwards.