Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (4th Edition)

Published by Pearson
ISBN 10: 0133942651
ISBN 13: 978-0-13394-265-1

Chapter 4 - Kinematics in Two Dimensions - Exercises and Problems: 10

Answer

(a) $r = (-3.0~\hat{i}+7.3~\hat{j})~m$ (b) $a = (-3.0~\hat{i}+8.0~\hat{j})~m/s^2$

Work Step by Step

$v(t) = (-3t~\hat{i}+2t^2~\hat{j})~m/s$ (a) $r(t) = r_0+\int_{0}^{t}~v(t)~dt$ $r(t) = r_0+\int_{0}^{t}~(-3t~\hat{i}+2t^2~\hat{j})~dt$ $r(t) = r_0+(-\frac{3}{2}t^2~\hat{i}+\frac{2}{3}t^3~\hat{j})~m$ At t = 2.0 s: $r = (3.0~\hat{i}+2.0\hat{j})~m+(-\frac{3}{2}(2.0)^2~\hat{i}+\frac{2}{3}(2.0)^3~\hat{j})~m$ $r = (3.0~\hat{i}+2.0\hat{j})~m+(-6.0~\hat{i}+\frac{16.0}{3}~\hat{j})~m$ $r = (-3.0~\hat{i}+\frac{22.0}{3}~\hat{j})~m$ $r = (-3.0~\hat{i}+7.3~\hat{j})~m$ (b) $a(t) = \frac{dv}{dt}$ $a(t) = (-3~\hat{i}+4t~\hat{j})~m/s^2$ At t = 2.0 s: $a = (-3.0~\hat{i}+(4.0)(2.0)~\hat{j})~m/s^2$ $a = (-3.0~\hat{i}+8.0~\hat{j})~m/s^2$
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