A. Motion, Speed, and Velocity
1. What does it mean to say motion is relative?
2. When describing everyday motion, what is usually used as a frame of reference?
3. Explain the difference between average speed and instantaneous speed?
4. Name two things that could be used to determine the instantaneous speed of a car?
5. Explain one thing that always makes speed differ from velocity.
6. If the speedometer in your car reads a constant 40 km/h, can you say the car is traveling at a constant velocity? Why or why not?
7. Speed is the rate at which ______changes.
8. Velocity is the rate at which ______changes.
9. While riding in a car with a friend, the friend is pulled over for speeding. The officer states, “Your friend was driving 43 miles per hour in a 35 mph zone.” Your friend tells the officer he shouldn’t receive a ticket because his average speed was just 30 mph. Explain the error in your friends thinking.
10. (I) A rabbit is at a position x = 3 m, some time later the rabbit is at a position x = 40 m. What is the displacement of the rabbit?
11. (I) Connor leaves his house at position x = 0 m to walk to the store at position x = 150 m. After visiting the store, Connor walks to his friend’s house at position x = -30 m.
a. Did Connor pass his house on his way to his friend’s house?
b. What was the distance traveled by Connor on his walk?
c. What was Connor’s displacement on his walk?
12. (I) A runner travels a distance of 400 m in a time of 65 s. What is the average speed of the runner?
13. (I) A girl on a bicycle traveling at a constant speed of 8 m/s. How long will it take her to ride 240 m?
14. (II) Concord is 35 km from MPHS. Patrick leaves school at 3:00 and reaches Concord at 3:20. What is Patrick’s average speed in km/h? m/s?
15. (II) While traveling on an interstate highway Rebecca sets her cruise control at 90 km/h. How far will she travel in 50 minutes?
16. (II) A dog is playing in the park. The dog starts at position x1 = 5 m and runs to position x2 = 30 m in a time of 10 s. The dog then runs to x3 = -20 m in 30 s.
a. Calculate the dog’s average speed from x1 to x2.
b. Calculate the dog’s average speed from x1 to x3.
c. Calculate the dog’s average velocity from x1 to x3. What is the direction of the dog’s average velocity?
17. (I) You are walking at a constant velocity of 2 m/s to the left while riding on a train that is moving at 12 m/s to the right.
a. What is your velocity relative to the train?
b. What is your velocity relative to the ground?
1. It depends on what is used as a frame of reference. / 2. the Earth’s surface/ 3. Instantaneous speed is at a given instant in time; average is calculated over a time interval. / 4. speedometer; radar gun
5. Velocity has a direction. (Speed is a scalar; velocity is a vector.) / 6. No. The car could be changing directions. / 7. distance / 8. position/displacement
9. Ask instructor about your answer during question time. / 10. 37 m / 11. a. yes b. 330 m c. -30 m / 12. 6.154 m/s
13. 30 s / 14. 105.0 km/h or
29.17 m/s / 15. 75.00 km or 7.500 x 104 m / 16. a. 2..500 m/s
b. 1.875 m/s
c. -0.6250 m/s, left
17. a. 2.000 m/s left
b. 10.00 m/s right
B. Accelerated Motion (Horizontal)
1. Acceleration is the rate at which ______changes.
2. Explain how a car traveling at a constant speed in a circular path is accelerating.
3. What is the acceleration of an object moving at a constant speed in a straight line?
4. A friend states the following controls inside a car will cause it to accelerate: gas pedal, brake, cruise control, headlight switch, and the steering wheel. Which ones are correct and why? Which ones are incorrect and why? Did your friend miss any?
5. (I) A car starts from rest and reaches a speed of 42 m/s over a 7.0 s period. What is the car’s acceleration?
6. (I) What rate of acceleration is needed for an object to increase it speed from 32 m/s to 96 m/s in 8.0 seconds?
7. (I) A car moving at 20 m/s is accelerated uniformly at a rate of 1.6 m/s2 for 6.8 s. What is the speed of the car at the end of the 6.8 s time period?
8. (II) A car comes to a stop after a uniform deceleration of 9.0 m/s2 for 8.0 s. What distance is traveled by the car during this time?
9. (II) During takeoff a plane (initially at rest) travels a distance of 500 m while being accelerated at a rate of 5.0 m/s2. What is the speed of the plane at takeoff?
10. (II) Determine the displacement of a plane as it is accelerated from 66 m/s to 88 m/s in 12 s.
11. (II) A rocket powered sled can start from rest reach a speed of 444 m/s in 1.80s and be brought to a stop again in 2.15 s.
a. What is the acceleration of the sled when starting?
b. What is the acceleration of the sled when braking?
1. Velocity / 2. It is changing directions / 3. 0 m/s2 / 4. Yes: gas pedal, brake steering wheelNo: cruise control. Light switch / 5. 6.000 m/s2 / 6. 8.000 m/s2
7. 30.88 m/s / 8. 288.0 m / 9. 70.71 m/s / 10. 924 m / 11. a. 246.7 m/s2 b. −206.5 m/s2
C. Accelerated Motion (Free Fall)
1. What is the rate of acceleration of an object experiencing free fall?
2. For an object thrown upward,
a. what is its speed at its highest point?
b. what is its acceleration at its highest point?
3. A toy rocket is launched straight up with an initial speed of 20 m/s. Neglecting air resistance, what is the velocity of the rocket as it impacts the ground?
4. When a falling object stops accelerating it has reached ______.
5. What causes a falling object to stop accelerating?
6. If gravity causes all falling object to accelerate at the same rate, why do some objects fall faster than others?
7. A student drops a stone from a bridge 120 m high.
a. With what velocity does the stone strike the water below?
b. How long does it take the stone to reach the water below?
8. (I) A stone starts from rest and falls freely for 8.0 s.
a. Calculate the speed of the stone at the end of the 8 s.
b. What distance does the stone travel during this time?
9. (II) A weather balloon is floating at a constant height above the ground when it releases a pack of instruments.
a. If the pack hits the ground at a speed of 73.5 m/s, what is the height of the balloon?
b. How long does it take the pack to fall from the balloon to the ground?
10. (II) A wrench falls from a helicopter rising at a constant speed of 6.0 m/s.
a. After 2 s, what is the velocity of the wrench?
b. After 2 s, how far below the helicopter is the wrench?
11. (II) An arrow is shot straight up from a height of 1.50 m with an initial speed of 45 m/s.
a. How long before the arrow reaches its maximum height?
b. What is the maximum height the arrow reaches?
c. What is the velocity of the arrow when it returns to the point where it was launched?
d. How long after launch does the arrow returns to its original height?
1. −9.8 m/s2 / 2. a) 0 m/sb) −9.8 m/s2 / 3. −20 m/s / 4. terminal velocity / 5. When air resistance pushing up equals the force of gravity pulling down on an object.
6. Some objects reach terminal velocity before others.
/ 7. a. −48.50 m/s
b. 4.949 s / 8. a. 78.4 m/s
b. 313.6 m / 9. a. 275.6 m
b. 7.50 / 10. a. −13.60 m/s b. 19.60 m below the helicopter
D. Motion Diagrams
Draw a motion diagram for the following situations. (See Instructor for Solutions)
1. (I) A car starts from rests and speeds up at a constant rate while moving right.
2. (I) A dog running at a constant speed.
3. (II) A ball is thrown straight up into the air and returns to the height it was thrown.
4. (II) A young child on a sled accelerates down a hill then moves at constant speed upon reaching flat ground at the bottom of the hill.
5. (II) A cyclist moving left and accelerating right.
E. Constructing/Analyzing Motion Graphs
1. Robin, roller skating down a marked sidewalk, was observed to be at the following positions at the times listed in the data table below. Graph the data (don’t forget labels) and answer the related questions. (See Instructor for Solutions)
Time(s) / Position (m) / / a) How far from the origin was he at t = 6.0 s? ______
0.0 / 10.0
1.0 / 12.0
2.0 / 14.0
5.0 / 20.0 / b) Was his speed constant over the entire interval? How do you know?
8.0 / 26.0
10.0 / 30.0
c) How fast was he traveling from t = 2.0 s to t = 8.0 s?
2. For each position-time graph, describe the motion and draw the corresponding velocity-time graph. (See Instructor for Solutions)
Position-Time Graph / Description of the Motion / Velocity-Time GraphConsider the motion given by the position-time graph shown below to answer questions 3-11.
3. (I) Is the object ever at rest? ______If so, when? ______
4. (I) Where is the object at the end of this trip? ______
5. (I) When is the object going the fastest? ______
6. (II) Are there any times during which the object is moving at the same speed? ______
If so, when? ______
7. (II) Are there any times during which the object is moving with the same, (nonzero) velocity? ______
If so, when? ______
8. (II) What is the average speed of the object for the entire trip? ______
9. (II) What is the average velocity for the object for the first 10 seconds? ______
10. (II) What is the instantaneous velocity at t = 15 s? ______
11. (II) Draw the velocity-time graph for the same motion illustrated in the position-time graph above.
+
Velocity (m/s) 0
-
0 5 10 15 20 25 30
Time (s)
3) yes t = 5s – 10s and t = 20s – 25s / 4) position +20 m / 5) t = 0s – 5s6) yes t = 10s – 20s and t = 25s – 30s / 7) no / 8) 2.00 m/s
9) +3.00 m/s / 10) – 2.00 m/s / 11) See Instructor
Consider a new motion … given by the velocity-time graph shown below … to answer questions 12 - 19.
12. (I) When was the object moving with constant speed? ______
13. (I) When was the object at rest? ______
14. (I) Was the object ever moving left? ______If so, when? ______
15. (I) What was the velocity of the object at t = 1 s? ______at t = 5 s? ______
16. (II) What was the acceleration of the object during the first 2 s? ______
17. (II) What was the displacement for the first 8 s? ______
18. (II) What was the displacement for the entire trip? ______
19. (II) Draw the acceleration-time graph for the same motion represented by the velocity-time graph above.
a (m/s2)
0
0 4 8 12 16 20
Time (s)
12) t = 2s – 8s t = 16s – 18s / 13) t = 10s – 14s / 14) t = 14s – 20s15) 1m/s; 2m/s / 16) 1m/s2 / 17) 14m
18) 8m / 19) See Instructor
F. Mixed Problems (See Instructor for Solutions)
1. (I) A car starts from rest and accelerates at a rate of 3.00 m/s2 for 10.0 s. What is the velocity of the car at the end of the 3 s?
Mathematical SolutionMotion Diagram
Position Vs Time
Velocity Vs Time
Acceleration Vs Time
2. (II) A bullet is fired straight up with a velocity of 275 m/s.
a. How long before the bullet reaches its highest point?
b. What is the maximum height the bullet reaches above where it was fired?
c. How much time elapses before the bullet returns to the launch point?
d. What is the distance traveled by the bullet?
G.
Mathematical SolutionMotion Diagram (vertical)
Position Vs Time
Velocity Vs Time
Acceleration Vs Time
3. (II) A car starts from rest (at position x=0) and accelerates at a rate of -2.5 m/s2 for 5 seconds. The car then travels at a constant velocity for 15 seconds before slowing to a stop during the next 10 seconds.