College Physics (7th Edition)

Published by Pearson
ISBN 10: 0-32160-183-1
ISBN 13: 978-0-32160-183-4

Chapter 2 - Kinematics: Description of Motion - Learning Path Questions and Exercises - Conceptual Questions - Page 59: 11


\begin{align*} a_A=2a_B \end{align*}

Work Step by Step

As we know from the equation of kinematics, the final velocity of Car A is given by \begin{align*} v_A^2=u_A^2+2a_A(d)\tag{1} \end{align*}and the final velocity of Car B is from \begin{align*} v_B^2=u_B^2+2a_B(2d)\tag{2} \end{align*}Both the cars start from rest, So, $u_A=u_B$. Also, both cars cross the starting line at the same time - $v_A=v_B$. Combining equations 1 and 2, we get \begin{align*} 2a_A(d)=2a_B(2d) \end{align*}\begin{align*} or, a_A=2a_B \end{align*}
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