Fundamentals of Physics Extended (10th Edition)

Published by Wiley
ISBN 10: 1-11823-072-8
ISBN 13: 978-1-11823-072-5

Chapter 2 - Motion Along a Straight Line - Problems - Page 38: 92c

Answer

The graph is shown in the picture.

Work Step by Step

We have the information of the distance $d = 1100m$, first-half acceleration $a1 = +1.2m/s^{2}$, and second-half acceleration $a2 = -1.2m/s^{2}$. To draw a graph without using a computer, we have to know the properties of the function. Let's start with the easiest one, which is the acceleration graph. The $a$ vs $t$ graph is a horizontal line in the time interval when the acceleration occurs. For $a1$, the time interval is from $t0 = 0$ to $t1 = \sqrt {d/a1} = 30.3s$. For $a2$, the time interval is from $t1 = 30.3s$ to $t2 = 2\times t1 = 60.6s$. The $v$ vs $t$ graph is a straight line with a positive gradient, which is $a1$, from $t0$ to $t1$; and a straight line with a negative gradient, which is $a2$, from $t1$ to $t2$. The $x$ vs $t$ graph is a quadratic curve: the first part from $t0$ to $t1$ is part of an opens-up quadratic function because it starts slowly and grows faster as time goes on (it's accelerating). the second part from $t1$ to $t2$ is part of an open-down quadratic function because it starts fast and slows down as time goes on (it's decelerating).
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