College Physics by Openstax Chapter 2 Problem 59: Verification of Jet Car Velocity and Acceleration Using Slopes of Position–Time and Velocity–Time Graphs

Problem:

(a) By taking the slope of the curve in Figure 2.60, verify that the velocity of the jet car is 115 m/s at t=20 s. (b) By taking the slope of the curve at any point in Figure 2.61, verify that the jet car’s acceleration is 5.0 m/s² .

Solution:

Part A

Figure A shows the approximate slope of the curve at time 20 seconds.

To solve for the slope of this line, we need to approximate by using two points. In this case, we shall use the points at time 15 seconds and 25 seconds.

Approximately, when $t=15\ \text{s}$ , the position is $x=1000\ \text{m}$ , and when $t=25\ \text{s}$ , the position is $x=2150\ \text{m}$ . Thefore,

\begin{align*} \text{velocity }& = \text{slope} \\ v& = \frac{\Delta x}{\Delta t} \\ v& = \frac{x_2-x_1}{t_2-t_1} \\ v& = \frac{2150\ \text{m}-1000\ \text{m}}{25\ \text{s}-15\ \text{s}}\\ v& = 115\ \text{m/s} \ \qquad \ {\color{DarkOrange} \left( \text{Answer} \right)} \end{align*}

Part B

One can immediately figure out from the given graph that it is a straight line. The slope of the line can be computed by using any two points in the line.

Here, $v=15\ \text{m/s}$ when $t=0\ \text{s}$ , and $v=40 \ \text{m/s}$ when $t=5\ \text{s}$ . The acceleration is

\begin{align*} \text{acceleration}& = \text{slope} \\ a& = \frac{\Delta v}{\Delta t}\\ a& = \frac{v_2-v_1}{t_2-t_1} \\ a& = \frac{40\ \text{m/s}-15\ \text{m/s}}{5\ \text{s}-0\ \text{s}}\\ a& = 5.0\ \text{m/s}^2 \ \qquad \ {\color{DarkOrange} \left( \text{Answer} \right)} \end{align*}

College Physics Chapter 2 Problems

Problem 1	Problem 2	Problem 3	Problem 4	Problem 5
Problem 6	Problem 7	Problem 8	Problem 9	Problem 10
Problem 11	Problem 12	Problem 13	Problem 14	Problem 15
Problem 16	Problem 17	Problem 18	Problem 19	Problem 20
Problem 21	Problem 22	Problem 23	Problem 24	Problem 25
Problem 26	Problem 27	Problem 28	Problem 29	Problem 30
Problem 31	Problem 32	Problem 33	Problem 34	Problem 35
Problem 36	Problem 37	Problem 38	Problem 39	Problem 40
Problem 41	Problem 42	Problem 43	Problem 44	Problem 45
Problem 46	Problem 47	Problem 48	Problem 49	Problem 50
Problem 51	Problem 52	Problem 53	Problem 54	Problem 55
Problem 56	Problem 57	Problem 58	Problem 59	Problem 60
Problem 61	Problem 62	Problem 63	Problem 64	Problem 65
Problem 66