Solutions Manual
Engineering Mechanics: Dynamics
3rd Edition
By
Gary L. Gray
Francesco Costanzo
Michael E. Plesha
All Chapters 12-20 (Dynamics Part)
Solutions Manual Download Link at The
End of This File.
,12-0 Solutions Manual
Chapter 12
Solutions
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw August 20, 2021
Hill LLC.
,Dynamics 3e 12-1
Problem 12.1
If 𝑣⃗avg is the average velocity of a point 𝑃 over a given time interval, is |𝑣⃗avg |, the magnitude of the average
velocity, equal to the average speed of 𝑃 over the time interval in question?
Solution
In general, |𝑣⃗avg | is not equal to 𝑣avg . To see this, consider a car that drives along a loop of length Δ𝐿 over a
time interval Δ𝑡 such that the departure and arrival points coincide. Since the departure and arrival positions
coincide, 𝑣⃗avg is equal to zero. This, implies that |𝑣⃗avg | is also equal to zero. By contrast, the average speed
will be different from zero because it is equal to the ratio Δ𝐿∕Δ𝑡.
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw August 20, 2021
Hill LLC.
, 12-2 Solutions Manual
Problem 12.2
A car is seen parked in a given parking space at 8:00 A .M . on a Monday morning and is then seen parked
in the same spot the next morning at the same time. What is the displacement of the car between the two
observations? What is the distance traveled by the car during the two observations?
Solution
The displacement is equal to zero because the difference in position over the time interval considered is equal
to zero. As far as the distance traveled is concerned, we cannot determine it from the information given. To
determine the distance traveled we would need to know the position of the car at every time instant during
the time interval considered instead of just at the beginning and end of the time interval in question.
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw August 20, 2021
Hill LLC.
Engineering Mechanics: Dynamics
3rd Edition
By
Gary L. Gray
Francesco Costanzo
Michael E. Plesha
All Chapters 12-20 (Dynamics Part)
Solutions Manual Download Link at The
End of This File.
,12-0 Solutions Manual
Chapter 12
Solutions
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw August 20, 2021
Hill LLC.
,Dynamics 3e 12-1
Problem 12.1
If 𝑣⃗avg is the average velocity of a point 𝑃 over a given time interval, is |𝑣⃗avg |, the magnitude of the average
velocity, equal to the average speed of 𝑃 over the time interval in question?
Solution
In general, |𝑣⃗avg | is not equal to 𝑣avg . To see this, consider a car that drives along a loop of length Δ𝐿 over a
time interval Δ𝑡 such that the departure and arrival points coincide. Since the departure and arrival positions
coincide, 𝑣⃗avg is equal to zero. This, implies that |𝑣⃗avg | is also equal to zero. By contrast, the average speed
will be different from zero because it is equal to the ratio Δ𝐿∕Δ𝑡.
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw August 20, 2021
Hill LLC.
, 12-2 Solutions Manual
Problem 12.2
A car is seen parked in a given parking space at 8:00 A .M . on a Monday morning and is then seen parked
in the same spot the next morning at the same time. What is the displacement of the car between the two
observations? What is the distance traveled by the car during the two observations?
Solution
The displacement is equal to zero because the difference in position over the time interval considered is equal
to zero. As far as the distance traveled is concerned, we cannot determine it from the information given. To
determine the distance traveled we would need to know the position of the car at every time instant during
the time interval considered instead of just at the beginning and end of the time interval in question.
© McGraw Hill LLC. All rights reserved. No reproduction or distribution without the prior written consent of McGraw August 20, 2021
Hill LLC.
