Question

If a ball is thrown into the air with a velocity of $ 40 ft/s $, its height in feet $ t $ seconds later is given by $ y = 40t - 16t^2 $. (a) Find the average velocity for the time period beginning when $ t = 2 $ and lasting (i) 0.5 seconds (ii) 0.1 seconds (iii) 0.05 seconds (iv) 0.01 seconds (b) Estimate the instantaneous velocity when $ t = 2 $.

   If a ball is thrown into the air with a velocity of $ 40 ft/s $, its height in feet $ t $ seconds later is given by $ y = 40t - 16t^2 $.

(a) Find the average velocity for the time period beginning when $ t = 2 $ and lasting
     (i) 0.5 seconds             (ii) 0.1 seconds
   (iii) 0.05 seconds          (iv) 0.01 seconds
(b) Estimate the instantaneous velocity when $ t = 2 $.

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Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition

Chapter 2, Problem 5

Instant Answer

Solved by Expert Mary Wakumoto

05/20/2022

Step 1

In this case, the displacement is the difference in height at time $ t $ and at $ t = 2 $, and the time is $ t - 2 $. So, the average velocity is given by \[ \frac{y(t) - y(2)}{t - 2} = \frac{40t - 16t^2 - 16}{t - 2} \] Show more…

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If a ball is thrown into the air with a velocity of $ 40 ft/s $, its height in feet $ t $ seconds later is given by $ y = 40t - 16t^2 $. (a) Find the average velocity for the time period beginning when $ t = 2 $ and lasting (i) 0.5 seconds (ii) 0.1 seconds (iii) 0.05 seconds (iv) 0.01 seconds (b) Estimate the instantaneous velocity when $ t = 2 $.

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