Motion and Speed Notes

Acceleration

Acceleration is the rate of change in velocity.

• Positive acceleration: Speed is increasing.
• Negative acceleration: Speed is decreasing.
• An object accelerates when it changes speed or direction.

Calculating Acceleration

• Acceleration is calculated as the change in velocity divided by time:
  $Acceleration = \frac{change \, in \, velocity}{time}$
• Change in velocity is the final velocity minus the initial velocity:
  $Change \, in \, velocity = final \, velocity - initial \, velocity$
• The unit for acceleration is meters per second squared ($m/s^2$).
• Positive acceleration is represented by a positive number and a positive slope on a velocity-time graph.
• Negative acceleration is represented by a negative number and a negative slope on a velocity-time graph.

Example: Roller coasters exemplify acceleration due to changes in speed and direction. Swaying on a wooden roller coaster is also a form of acceleration because it involves a change in direction.

Motion and Forces

A force is a push or pull that one body applies to another.

• A force can cause an object's motion to change.
• When two or more forces combine, they create a net force.
• Balanced forces are equal in size and opposite in direction.
• Unbalanced forces are unequal in size and/or not in the same direction.

Inertia and Mass

• Inertia is an object's resistance to any change in its motion.
• Objects with greater mass have greater inertia.
• Newton's first law of motion states that an object moving at a constant velocity keeps moving at that velocity unless a net force acts on it; an object at rest will stay at rest unless a net force acts on it.

Example: Auto Crashes and Inertia

• A passenger not wearing a seat belt keeps moving forward at the car's speed even after the car stops due to inertia.
• A passenger wearing a seat belt slows down as the car slows down and stops because the seatbelt provides the force needed to overcome inertia.

A glass full of water requires more force to pick up than an empty glass because the full glass has greater mass and therefore greater inertia.

Hands-On Activities

MiniLab

Average speed is calculated as distance divided by time. The speed remains the same regardless of the direction of travel.

MiniLab: Try at Home

1. Without rubber bands, the forces acting on an object on a cart are gravity and the force exerted by the cart. When the cart hits a wall, the object continues moving until a stop block exerts a force. Rubber bands exert an additional force, stretching and slowing the object over a longer period, reducing the stopping force.
2. Seat belts reduce stopping force and decrease passenger damage during a crash.

Activity

• Goggles are a safety precaution to prevent injury if the spring scale comes loose.
• Newton's first law states that an object at rest remains at rest until acted upon by a net unbalanced force.

Conclude and Apply

1. As force increases, acceleration increases.
2. Adding a second book should double the force if the books have approximately the same mass.

Activity: Design Your Own Experiment

• Goggles are recommended for eye protection during laboratory activities.
• Objects with greater mass require more force to move; therefore, a basketball requires more force than a tennis ball.

Analyze Your Data

1. Graphs may show a slight increase or decrease in speed.
2. Average speed is calculated using $v = d/t$.

Laboratory Activities

Laboratory Activity 1

Questions and Conclusions

1. Constant force results in constant acceleration.
2. The rate of acceleration remained constant.
3. Acceleration decreases as mass increases.
4. As force increases, acceleration increases.
5. No movement indicates that the skater's inertia was too great, requiring a force greater than 4-N to move.
6. Student answers will vary, but the notion should be rejected.

Laboratory Activity 2

Questions and Conclusions

1. Faster trials have steeper slopes, slower trials have flatter slopes.
2. Slope indicates the speed of the object; a larger slope indicates faster travel, and a smaller slope indicates slower travel.
3. A horizontal line indicates that the object has stopped.
4. A bowling ball dropped from a great height would fall at a constant rate of $9.8 \, m/s^2$, while the bowling ball in the lab negatively accelerated.
5. Student answers will vary.
6. Student answers will vary.
7. Distance is how far an object moves, while displacement is the distance and direction of the object from the starting point.

Directed Reading for Content Mastery

Overview

1. velocity
2. speed
3. position
4. direction
5. unbalanced
6. greater
7. direction
8. negative

Section 1

1. b
2. a
3. b
4. a
5. a
6. b
7. a
8. c

• Yes
• Answers will vary.
• Answers will depend on student hypothesis.

Sections 2 and 3

1. velocity
2. positive
3. negative
4. direction
5. time
6. acceleration
7. d
8. e
9. c
10. a
11. f
12. b

Reinforcement

Section 1

1. e
2. b
3. a and c
4. d
5. walking home
6. An object has moved because its position has changed.
7. Displacement is how far and in what direction an object has moved from its starting point.
8. Instantaneous speed indicated on the speedometer.
9. A horizontal line on a distance-time graph indicates that an object is stationary.
10. Speed is calculated by dividing the time elapsed by the distance moved.
11. A race car driving around a track at 240 km/h can have a constant speed.

Section 2

1. Acceleration is the rate of change of velocity.
2. An object accelerates when it changes its speed and/or direction.
3. Positive acceleration occurs when an object's speed increases; negative acceleration occurs when an object's speed decreases.
4. Change in velocity (final velocity minus initial velocity) divided by time.
5. meters/second/second; meters/second²
6. acceleration
7. $a = (v) = (9 \, m/s - 3 \, m/s)/3s = 2 \, m/s^2$
8. positive
9. negative
10. zero

Section 3

1. Force is a push or a pull that one object exerts on another.
2. Answers will vary. Examples might include fingers on pencil; body on chair; feet on floor; atmosphere on body.
3. The direction of the motion will change in the direction of the force.
4. It is the net force.
5. The forces are balanced.
6. The forces acting on the rock are not balanced; the net force is not zero.
7. It is the tendency of an object to resist any change in its motion.
8. Velocity changes when the object speeds up, slows down, or changes direction.
9. Its mass determines its inertia.
10. An object moving at constant velocity continues to move at that velocity until a net force acts on it.

Enrichment

Section 1

1. The runners are supposed to run 400 meters. Because the track is wider at the outer edges, only the inside track is 400 m long. The other runners start at a distance of 400 m from the finish line.
2. The runner in lane one (the inside lane) has zero displacement because that runner ends the race in the same position in which she or he started. The displacement of the other runners will vary.
3. Average speed for runner number four would be $9.0 \, m/s$. $v = d/t = 400 \, m/44.40 \, s = 9.0$

Section 2

1. Both planes are flying at the same altitude with the same velocity and will crash if they do not change. NJ446 should maintain current velocity or negatively accelerate, and DL267 should accelerate.
2. Student answers will vary but should show an understanding of how negative acceleration or other change in velocity will keep the planes from colliding.
3. Flight A334 is at an altitude that is lower than the others and is not on a collision course with either plane.

Section 3

1. Student answers will vary but should demonstrate an understanding of how forces affect inertia.
2. As the car moves forward, the seat (which is attached to the car) pushes the passengers forward. As the car moves, the seat moves. And as the seat moves, the passengers move.
3. Crumple zones are designed to absorb some of the energy from the impact of the crash.

Chapter Review

Part A. Vocabulary Review

1. balanced forces
2. negative acceleration
3. net force
4. average speed
5. slope
6. speed
7. force
8. displacement
9. inertia
10. distance
11. velocity
12. instantaneous speed
13. acceleration

Part B. Concept Review

1. a. Both are lengths. Distance is a measurement of how far an object has moved; displacement is the distance and direction of an object's change in position from the starting point.
   b. Both are measured in m/s. Speed is distance over time; velocity includes speed of an object and direction of its motion.
2. An object with positive acceleration has increasing speed; an object with negative acceleration has decreasing velocity.
3. It takes a net unbalanced force to change motion.
4. It is related to mass.
5. $v = d/t = 240 \, km/4h = 60 \, km/h$
6. $a = vv = (0-9 \, m/s)/3 \, s = -3 \, m/s^2$. The acceleration is $-3 \, m/s^2$.
7. The unrestrained passenger continues forward because of inertia. The car encountered another force, but the passenger did not.
8. The car negatively accelerates, reaches a constant speed, and then negatively accelerates to a stop.
9. The rider negatively accelerates nearly to a stop, cruises at a slow but constant speed, then rapidly accelerates.

Chapter Test

I. Testing Concepts

1. 1
2. a
3. b
4. i
5. j
6. h
7. k
8. c
9. g
10. d
11. f
12. e
13. m
14. p
15. o
16. q
17. n

II. Understanding Concepts

1. The bike rider moved away from his starting point at a regular pace, stopped moving for a period of time, then returned home at a slower speed.
2. The object in graph two traveled at a constant speed to a point, then negatively accelerated until it reached zero acceleration.
3. Graph one is labeled "distance" and "time." This graph represents how far one person traveled in a given time. Graph two is labeled "speed" and "time." This graph is measuring an object's speed as it traveled.
4. No, the graphs cannot represent the same objects because they accelerate at different points and negatively accelerate at different points.
5. inertia
6. negative
7. speed; direction
8. speed
9. distance
10. final velocity
11. negative; positive
12. negative
13. unbalanced force
14. mass
15. zero
16. inertia

III. Applying Concepts

1. Their displacements are equal if both people travel the same distance in the same direction.
2. Yes, the direction of the book could be changing.
3. No, any change in speed will change the velocity.
4. a. $2(1m+ 3m) = 8m$
   b. zero
5. $s = d/t = 5.20 \, m/10.4 \, s = 0.5 \, m/s$
6. $(vj− v₁)/t − (2m - 16 \, m)/3.5 \, s = 4.0 \, m/s^2$

IV. Writing Skills

1. Yes, it can change. By definition, when a car is accelerating, its velocity is changing. Acceleration is constant when the car is speeding up at a constant rate.
2. The hands of a clock are constantly changing their direction, so they travel at constant speed but not at constant velocity.
3. Answers may vary. The student first stands still and has zero acceleration. Then she starts to move with positive acceleration, then slows down with negative acceleration and comes to a stop again. This pattern continues until the student is through the line.
4. An object will only accelerate if there is an net unbalanced force acting on it. There may be many forces acting upon an object, but if the net force is zero, the object will not accelerate.
5. No, it simply means that the velocity is constant. The object will not change its motion.
6. The horse stopped, but the rider's body was not firmly attached to the horse, so the rider's inertia caused him to continue his motion in the forward direction and sail over the horse's head.

Transparency Activities

Section Focus Transparency 1

Teaching Tips

• Define speed as the time it took to travel a certain distance (speed = distance / time).
• Velocity incorporates speed and direction. A change in velocity occurs when an object changes speed or direction.

Content Background

• Instantaneous speed is the speed of an object at a specific moment.
• Average speed is determined by dividing distance traveled by time.
• Acceleration is the change in speed or direction (velocity).

Answers to Student Worksheet

1. Answers will vary. The rabbit had the faster top speed, but the tortoise eventually won the race, meaning the tortoise's average speed was greater.
2. The car speeds up in straightaways and slows down in turns. The direction the car is travelling changes in turns.

Section Focus Transparency 2

Teaching Tips

• Skiers reaching speeds of 224 km/h exemplify acceleration. Discuss gravity, acceleration, friction, and air resistance.
• Define drag (aerodynamic force resisting forward motion) and discuss how shape affects drag and acceleration.
• Discuss drag reduction in sports: sprinters staying low, hockey players crouching, streamlined racecars, and drafting.

Content Background

• Newton's second law: force causes acceleration in the direction of the force (gravity for skiers).
• Drag inhibits forward movement. Friction and wind are types of drag.
• Waxing skis and snowboards reduces drag, increasing speed.

Answers to Student Worksheet

1. Answers will vary. The racer will speed up, slow down, and change direction.
2. Gravity pulls the skier downhill. Speed increases until balanced by air resistance and ski friction.
3. A tuck reduces air resistance (drag), increasing speed.

Section Focus Transparency 3

Teaching Tips

• Introduce the connection between force and motion using a tennis ball.
• A force is a push or pull exerted by one object on another.
• Explain the ball's motion as a result of applied forces, including gravity.
• Discuss why there is little rope movement when forces are equal in tug-of-war.

Content Background

• Newton's first law (inertia): objects in motion stay in motion unless acted on by a net force.

Answers to Student Worksheet

1. The other team pulls in the opposite direction.
2. One side pulled harder, resulting from unbalanced forces.
3. Heavier teams are harder to move due to inertia.

Teaching Transparency

Distance-Time Graph

• Review the x-axis (time) and y-axis (distance).
• Review independent and dependent variables.

Answers to Student Worksheet

1. time in minutes
2. five
3. meters
4. The slopes of the lines give you the speeds of the swimmers.
5. The swimmer represented by the red line swam the fastest. The green-line swimmer stopped for ten minutes.
6. 900 m
7. The fastest swimmer traveled 1,200 meters farther than the slowest swimmer.