Physics for Scientists and Engineers with Modern Physics
Physics for Scientists and Engineers with Modern Physics
10th Edition
ISBN: 9781337553292
Author: Raymond A. Serway, John W. Jewett
Publisher: Cengage Learning
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Textbook Question
Chapter 2, Problem 10P

(a) Use the data in Problem 3 to construct a smooth graph of position versus time. (b) By constructing tangents to the x(t) curve, find the instantaneous velocity of the car at several instants. (c) Plot the instantaneous velocity versus time and, from this information, determine the average acceleration of the car. (d) What was the initial velocity of the car?

(a)

Expert Solution
Check Mark
To determine

To draw: The graph of position versus time.

Answer to Problem 10P

Therefore, the smooth graph of position versus time is shown in Figure I.

Explanation of Solution

Given information:

The following table contains the data of position of the car at various time instants.

t(s) 0 1.0 2.0 3.0 4.0 5.0
x(m) 0 2.3 9.2 20.7 36.8 57.5

Draw the graph of position versus time for the derby car.

Physics for Scientists and Engineers with Modern Physics, Chapter 2, Problem 10P , additional homework tip  1

Figure I

In the shown graph, the position of the car at various time instants is plotted in the vertical axis against the time along horizontal direction.

Conclusion:

Therefore, the smooth graph of position versus time is shown in Figure I.

(b)

Expert Solution
Check Mark
To determine

The instantaneous velocity of the car at various time instants.

Answer to Problem 10P

The instantaneous velocity of the car at t=1s is 2.3m/s , at t=2s is 4.2m/s , at t=3s is 6.9m/s , at t=4s is 9.1m/s and at t=5.0s is 11.5m/s .

Explanation of Solution

Given information:

The following table contains the data of position of the car at various time instants.

t(s) 0 1.0 2.0 3.0 4.0 5.0
x(m) 0 2.3 9.2 20.7 36.8 57.5

Draw the tangent line at the time instant of t=1s in the graph of position versus time for the derby car.

Physics for Scientists and Engineers with Modern Physics, Chapter 2, Problem 10P , additional homework tip  2

Figure II

Formula to calculate the instantaneous velocity of the car at t=1s from the shown graph is,

vt=1s=x1t1

  • vt=1s is the instantaneous velocity of the car at t=1s .
  • x1 is the position of the car at t=1s .

Substitute 2.3m for x1 and 1s for t1 in the above equation to find vt=1s .

vt=1s=2.3m1s=2.3m/s

Therefore, the instantaneous velocity of the car at t=1s is 2.3m/s .

The following table contains the data of position of the car at various time instants.

t(s) 0 1.0 2.0 3.0 4.0 5.0
x(m) 0 2.3 9.2 20.7 36.8 57.5

Draw the tangent line at the time instant of t=2s in the graph of position versus time for the derby car.

Physics for Scientists and Engineers with Modern Physics, Chapter 2, Problem 10P , additional homework tip  3

Figure III

Formula to calculate the instantaneous velocity of the car at t=2s from the shown graph is,

vt=2s=x2t2

  • vt=2s is the instantaneous velocity of the car at t=2s .
  • x2 is the position of the car at t=2s .

Substitute 9.2m for x2 and 2s for t2 in the above equation to find vt=2s .

vt=2s=9.2m2s=4.6m/s

Therefore, the instantaneous velocity of the car at t=2s is 4.6m/s .

The following table contains the data of position of the car at various time instants.

t(s) 0 1.0 2.0 3.0 4.0 5.0
x(m) 0 2.3 9.2 20.7 36.8 57.5

Draw the tangent line at the time instant of t=3s in the graph of position versus time for the derby car.

Physics for Scientists and Engineers with Modern Physics, Chapter 2, Problem 10P , additional homework tip  4

Figure IV

Formula to calculate the instantaneous velocity of the car at t=3s from the shown graph is,

vt=3s=x3t3

  • vt=3s is the instantaneous velocity of the car at t=3s .
  • x3 is the position of the car at t=3s .

Substitute 20.7m for x3 and 3s for t3 in the above equation to find vt=3s .

vt=3s=20.7m3s=6.9m/s

Therefore, the instantaneous velocity of the car at t=3s is 6.9m/s .

The following table contains the data of position of the car at various time instants.

t(s) 0 1.0 2.0 3.0 4.0 5.0
x(m) 0 2.3 9.2 20.7 36.8 57.5

Draw the tangent line at the time instant of t=4s in the graph of position versus time for the derby car.

Physics for Scientists and Engineers with Modern Physics, Chapter 2, Problem 10P , additional homework tip  5

Figure V

Formula to calculate the instantaneous velocity of the car at t=4s from the shown graph is,

vt=4s=x4t4

  • vt=4s is the instantaneous velocity of the car at t=4s .
  • x4 is the position of the car at t=4s .

Substitute 36.8m for x4 and 4s for t4 in the above equation to find vt=4s .

vt=4s=36.8m4s=9.2m/s

Therefore, the instantaneous velocity of the car at t=4s is 9.2m/s .

The following table contains the data of position of the car at various time instants.

t(s) 0 1.0 2.0 3.0 4.0 5.0
x(m) 0 2.3 9.2 20.7 36.8 57.5

Draw the tangent line at the time instant of t=4s in the graph of position versus time for the derby car.

Physics for Scientists and Engineers with Modern Physics, Chapter 2, Problem 10P , additional homework tip  6

Figure VI

Formula to calculate the instantaneous velocity of the car at t=4s from the shown graph is,

vt=5s=x5t5

  • vt=5s is the instantaneous velocity of the car at t=5s .
  • x5 is the position of the car at t=5s .

Substitute 57.5m for x5 and 5s for t5 in the above equation to find vt=5s .

vt=5s=57.5m5s=11.5m/s

Conclusion:

Therefore, the instantaneous velocity of the car at t=5s is 11.5m/s .

(c)

Expert Solution
Check Mark
To determine

The average acceleration of the car.

Answer to Problem 10P

The average acceleration of the car is 2.3m/s2 .

Explanation of Solution

The following table contains the instantaneous velocity of the car at various times instant.

t(s) 1.0 2.0 3.0 4.0 5.0
v(t)m/s 2.3 4.6 6.9 9.2 11.5

The graph of instantaneous velocity versus time for the derby car is shown below.

Physics for Scientists and Engineers with Modern Physics, Chapter 2, Problem 10P , additional homework tip  7

Figure VII

The figure VII shows that velocity of the car increases linearly, it means the acceleration of the car is constant throughout the motion.

Thus, the slope of this graph gives the average acceleration of the car.

From the graph, the slope of the graph is 2.3m/s2 .

Conclusion:

Therefore, the average acceleration of the car is 2.3m/s2 .

(d)

Expert Solution
Check Mark
To determine

The initial velocity of the car.

Answer to Problem 10P

The initial velocity of the car is zero.

Explanation of Solution

The equation for the velocity of the car obtained from the graph is,

v(t)=(2.3m/s2)t (I)

The first equation of motion gives the velocity of an object at any instant.

v(t)=vi(t)+at (II)

  • vi(t) is the initial velocity of the car.

Compare equation (I) and (II).

vi(t)=0

Thus, the initial velocity of the car is zero.

Conclusion:

Therefore, the initial velocity of the car is zero.

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Chapter 2 Solutions

Physics for Scientists and Engineers with Modern Physics

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