PHYS103 Fall 2005 Homework 2

Giancoli Sixth Edition Chapter 2

Questions 1, 2, 3, 5, 7

Problems 1, 5, 7, 8, 13, 17, 19, 20

Answers to Questions

1. A car speedometer measures only speed. It does not give any information about the direction, and so does not measure velocity.

2. By definition, if an object has a constant velocity, then both the object's speed and its direction of motion are constant. Therefore the object CANNOT have a varying speed if its velocity is constant.

3. When an object moves with constant velocity, its average velocity over any time interval is exactly equal to its instantaneous velocity at all times

5. There is no general relationship between the magnitude of speed and the magnitude of acceleration. For example, one object may have a large but constant speed. The acceleration of that object is then 0. Another object may have a small speed but be gaining speed, and therefore have a positive acceleration. So in this case the object with the greater speed has the lesser acceleration.

Or consider two objects that are dropped from rest at different times. If we ignore air resistance, then the object dropped first will always have a greater speed than the object dropped second, but both will have the same acceleration of 9.80 m/s².

7. If an object is traveling to the north but slowing down, it has a northward velocity and a southward acceleration.

Solutions to Problems

1. The average speed is given by:

.

5. The average velocity is given by .

7. The time for the first part of the trip is calculated from the initial speed and the first distance.

The time for the second part of the trip is therefore

The distance for the second part of the trip is calculated from the average speed for that part of the trip and the time for that part of the trip.

(a) The total distance is then

(b) The average speed is NOT the average of the two speeds. Use the definition of average speed.

8. The speed of sound is intimated in the problem as 1 mile per 5 seconds. The speed is calculated by:

.

Note that only 1 significant figure is given, (5 sec), and so only 1 significant figure is justified in the result.

13. The average speed for each segment of the trip is given by , so for each segment.

For the first segment, .

For the second segment, .

Thus the total time is .

The average speed of the plane for the entire trip is

.

17. (a) The average acceleration of the sprinter is .

(b)

19. The initial velocity of the car is the average speed of the car before it accelerates.

The final speed is , and the time to stop is 4.0 s. Use Eq. 2-11a to find the acceleration.

20. To estimate the velocity, find the average velocity over each time interval, and assume that the car had that velocity at the midpoint of the time interval. To estimate the acceleration, find the average acceleration over each time interval, and assume that the car had that acceleration at the midpoint of the time interval. A sample of each calculation is shown.

From 2.00 s to 2.50 s, for average velocity:

From 2.25 s to 2.75 s, for average acceleration: