A. Conceptual Ideas: Horizontal Motion

A. Conceptual Ideas: Horizontal Motion 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 the difference between speed and 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? 7. Name three controls in a car that allow the driver to change the velocity of the car. 8. Speed is the rate at which ______changes. 9. Velocity is the rate at which ______changes. 10. Acceleration is the rate at which ______changes. 11. Explain how a car traveling at a constant speed in a circular path is accelerating. 12. What is the acceleration of an object moving at a constant speed in a straight line?

1. It depends on what is 2. the Earth’s 3. Instantaneous speed is at a given 4. speedometer; used as a frame of surface instant in time; average is calculated radar gun reference. over a time interval. 5. Velocity has a direction. 6. No. The car (Speed is a scalar; velocity is could be changing 7. accelerator; brake; steering wheel 8. distance a vector.) directions. 9. position/displacement 10. velocity 11. It is changing directions. 12. 0 m/s2

B. Problems: Horizontal Motion 1. (I) 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? 2. (I) While traveling on an interstate highway Rebecca sets her cruise control at 90 km/h. How far will she travel in 50 minutes? 3. (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. 3.a.What is your velocity relative to the train? 3.b. What is your velocity relative to the ground? 4. (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? 5. (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? 6. (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? 7. (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? 8. (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? 9. (II) Determine the displacement of a plane as it is accelerated from 66 m/s to 88 m/s in 12 s. 10. (I) 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. 10.a. What is the acceleration of the sled when starting? 10.b. What is the acceleration of the sled when braking?

1 1) 105.0 km/h or 29.17 2) 75.00 km or 7.500 x 3) a. 2.000 m/s left 4) 6.000 m/s2 m/s 104 m b. 10.00 m/s right 5) 8.000 m/s2 6) 30.88 m/s 7) 288.0 m 8) 70.71 m/s

9) 924 m 10) a. 246.7 m/s2 b. −206.5 m/s2

C. Conceptual Ideas: Vertical (Free Fall) Motion 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?

1. −9.8 m/s2 2. a) 0 m/s b) −9.8 m/s2 3. −20 m/s 6. Some objects reach terminal velocity 4. terminal velocity 5. When air resistance pushing up equals the force of gravity pulling down on an before others. object.

D. Problems: Vertical (Free Fall) Motion 1. (I) 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? 2. (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? 3. (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? 4. (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? 5. (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?

2 1) a. −48.50 m/s b. 2) a. 78.4 m/s b. 3) a. 275.6 m b. 4) a. −13.60 m/s b. 19.60 m below 4.949 s 313.6 m 7.50 s the helicopter 5) a. 4.592 s b. 104.8 m c. −45 m/s d. 9.184 s

3 E. 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.

4 F. Drawing Motion Graphs

For each diagram below, construct the motion graphs that describe the motion of the ball as it rolls along the ramp. Assume that the ball does not experience a change in velocity while rolling on the horizontal portion of the track. (See Instructor for Solutions)

1. Motion Diagram

Position Vs Time

Velocity Vs Time

Acceleration Vs Time

5 2. Motion Diagram

Position Vs Time

Velocity Vs Time

6 3. Motion Diagram

Position Vs Time

Velocity Vs Time

7 4. Motion Diagram

Position Vs Time

Velocity Vs Time

8 5. Motion Diagram

Position Vs Time

Velocity Vs Time

9 G. 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 Position a) How far from the origin was he at t = 6.0 s? (s) (m) ______0.0 10.0 1.0 12.0 2.0 14.0 5.0 20.0 d) Was his speed constant over the entire interval? 8.0 26.0 How do you know? 10.0 30.0 g) 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 Graph

10 Consider 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

11 - 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 – 5s 6) yes t = 10s – 20s and t = 25s – 7) no 8) 2.00 m/s 30s 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.

12 a (m/s2)

0 4 8 12 16 20 Time (s)

12) t = 2s – 8s t = 16s – 18s 13) t = 10s – 14s 14) t = 14s – 20s 15) 1m/s; 2m/s 16) 1m/s2 17) 14m 18) 8m 19) See Instructor

H. 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 Solution

Motion Diagram

13 Position Vs Time

Velocity Vs Time

14 2. (II) A bullet is fired straight up with a velocity of 275 m/s.

2.a.How long before the bullet reaches its highest point?

2.b. What is the maximum height the bullet reaches above where it was fired?

2.c.How much time elapses before the bullet returns to the launch point?

2.d. What is the distance traveled by the bullet?

I. Mathematical Solution

Motion Diagram

Position Vs Time

Velocity Vs Time

15 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. a. What is the maximum velocity of the car? b. What is the displacement of the car during the 30 second period? c. What is the acceleration of the car during the last 10 seconds of travel?

Mathematical Solution

Motion Diagram

Position Vs Time

Velocity Vs Time

16 Acceleration Vs Time