Calculus

1) A ball is thrown into the air by a baby alien on a planet in the system of Alpha Centauri with a velocity of 50 ft/s. Its height in feet after t seconds is given by y=50t-26t^{2}.

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

.01 s:

.005 s:

.002 s:

.001 s:

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

B. Estimate the instantaneous velocity when t=1.

Answer:

2) The position of a cat running from a dog down a dark alley is given by the values of the table.

t (seconds) 0 1 2 3 4 5

s (feet) 0 5 44 61 99 120

A. Find the average velocity to the time period beginning when t=2 and lasting

1. 3 s

2. 2 s

3. 1 s

B. Estimate the instantaneous velocity when t=2 by finding the average velocity from t=1 to t=3: