Average velocity

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 35 ft/s. Its height in feet after t seconds is given by y=35t-30t^2. 

A. Find the average velocity for the time period beginning when t1=1 and lasting for the following number of seconds

.01 sec:

.005 sec:

.002 sec:

.001 sec:

For the above answers, you may have to enter 6 or 7 significant digits if you are using a calculator.

Estimate the instanteneous velocity when t=1.

Answer 1

Average velocity = (distance traveled)/(elapsed time)

For t₁ = 1 second and t₂ = 1.01 seconds:

Distance traveled = y(1.01) - y(1) = [35(1.01) - 30(1.01)²] - [35(1) - 30(1)²] = 4.747 - 5 = -0.253 feet

Elapsed time = 0.01 seconds

Average velocity = -0.253/0.01 = -25.3 ft/s

Repeat for t₂ = 1.005, t₂ = 1.002, and t₂ = 1.001 seconds