Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - 1.4 The Tangent and Velocity Problems - 1.4 Exercises - Page 50: 6


(a) (i) 4.42 m/s (ii) 5.35 m/s (iii) 6.094 m/s (iv) 6.2614 m/s (v) 6.27814 m/s (b) 6.28 m/s

Work Step by Step

The average velocity over the time interval $[t_{1},t_{2}]$ is equal to $\frac{y(t_{2})-y(t_{1})}{t_{2}-t_{1}}$. Therefore we can plug in respective values of $t_{1}$ and $t_{2}$ to find the average velocities. (a) (i) $t_{1}$ = 1s, $t_{2}$ = 2s, $v_{avg}$ = 4.42 m/s (ii) $t_{1}$ = 1s, $t_{2}$ = 1.5s, $v_{avg}$ = 5.35 m/s (iii) $t_{1}$ = 1s, $t_{2}$ = 1.1s, $v_{avg}$ = 6.094 m/s (iv) $t_{1}$ = 1s, $t_{2}$ = 1.01s, $v_{avg}$ = 6.2614 m/s (v) $t_{1}$ = 1s, $t_{2}$ = 1.001s, $v_{avg}$ = 6.27814 m/s (b) In part (a), it appears that the average velocities are approaching a value of 6.28 m/s as $t_{2}$ approaches 1s. So, an estimate of the instantaneous velocity when t=1 is 6.28 m/s.
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