# Chapter: Motion and Momentum

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Chapter: Motion and Momentum
Table of Contents 18 Chapter: Motion and Momentum Section 1: What is Motion? Section 2: Acceleration Section 3: Momentum

What is Motion? 1 Matter and Motion All matter in the universe is constantly in motion, from the revolution of Earth around the Sun to elections moving around the nucleus of an atom.

Changing Position 1 Something is in motion if it is changing position.
What is Motion? 1 Changing Position Something is in motion if it is changing position. It could be a fast-moving airplane, a leaf swirling in the wind, or water tricking from a hose. When an object moves from one location to another, it is changing position.

What is Motion? 1 Changing Position The runners sprint from the start line to the finish line. Their positions change, so they are in motion.

What is Motion? 1 Relative Motion An object changes position if it moves relative to a reference point. Picture yourself competing in a 100-m dash. You begin just behind the start line. When you pass the finish line, you are 100 m from start line.

What is Motion? 1 Relative Motion If the start line is your reference point, then your position has changed by 100 m relative to the start line, and motion has occurred.

Distance and Displacement
What is Motion? 1 Distance and Displacement Displacement includes the distance between the starting and ending points and the direction in which you travel. This figure shows the difference between distance and displacement.

What is Motion? 1 Speed Speed is the distance traveled divided by the time taken to travel the distance. Speed can be calculated from this equation:

What is Motion? 1 Speed In SI units, distance is measured in m and time is measured in s. As a result, the SI unit of speed is the m/s—the SI distance unit divided by the SI time unit.

What is Motion? 1 Average Speed Average speed is found by dividing the total distance traveled by the time taken. An object in motion can change speeds many times as it speeds up or slows down.

What is Motion? 1 Average Speed The speed of an object at one instant of time is the object's instantaneous speed. If it takes you 0.5 h to walk 2 km to the library, your average speed would be as follows:

What is Motion? 1 Average Speed Average speed, instantaneous speed, and constant speed are illustrated here.

You can represent the motion of an object with a distance-time graph.
What is Motion? 1 Graphing Motion You can represent the motion of an object with a distance-time graph. For this type of graph, time is plotted on the horizontal axis, and distance is plotted on the vertical axis. Click box to view movie.

Distance-Time Graphs and Speed
What is Motion? 1 Distance-Time Graphs and Speed Look at the graph. According to the graph, after 1 s student A traveled 1 m. Student B, however, traveled only 0.5 m in the first second.

Distance-Time Graphs and Speed
What is Motion? 1 Distance-Time Graphs and Speed So student A traveled faster than student B. The line representing the motion of student A is steeper than the line for student B.

Distance-Time Graphs and Speed
What is Motion? 1 Distance-Time Graphs and Speed A steeper line on the distance-time graph represents a greater speed. A horizontal line on the distance-time graph means that no change in position occurs.

What is Motion? 1 Velocity If you are hiking in the woods, you want to know not only your speed, but also the direction in which you are moving.

This is why a compass and a map are useful to hikers.
What is Motion? 1 Velocity The velocity of an object is the speed of the object and direction of its motion. This is why a compass and a map are useful to hikers.

What is Motion? 1 Velocity Velocity has the same units as speed, but it also includes the direction of motion. The velocity of an object can change if the object's speed changes, its direction of motion changes, or they both change.

Section Check 1 Question 1 To determine whether something has changed position, you need a _______. A. compass B. global positioning system C. map D. reference point

Section Check 1 Answer The answer is D. If someone starts a car and drives it 100 meters from its parking spot, the parking spot can be used as a point of reference to show that the car moved.

Section Check 1 Question 2 Displacement includes your _______ and _______ as well as the _______ in which you have traveled.

Section Check 1 Answer It includes your starting point, ending point, and direction in which you have traveled. It is possible to have traveled a great distance and still have a displacement of zero if you traveled in an enormous circle and ended right where you began.

Question 3 1 Speed equals distance divided by _______. A. force
Section Check 1 Question 3 Speed equals distance divided by _______. A. force B. mass C. time D. velocity

Section Check 1 Answer The answer is C. The smaller the t value in s=d/t, the greater the speed.

Acceleration and Motion
2 Acceleration and Motion Acceleration is the change in velocity divided by the time it takes for the change to occur. Acceleration has a direction. If an object speeds up, the acceleration is in the direction that the object is moving.

Acceleration and Motion
2 Acceleration and Motion If an object slows down, the acceleration is opposite to the direction that the object is moving. If the direction of the acceleration is at an angle to the direction of motion, the direction of motion will turn toward the direction of the acceleration.

When the speed of an object increases, it is accelerating.
Acceleration 2 Speeding Up When an object that is already in motion speeds up, it also is accelerating. When the speed of an object increases, it is accelerating. The toy car is accelerating to the right. Its speed is increasing.

Acceleration 2 Slowing Down Acceleration occurs when an object slows down, as well as when it speeds up. The car is slowing down. During each time interval, the car travels a smaller distance, so its speed is decreasing.

Motion is not always along a straight line.
Acceleration 2 Changing Direction Motion is not always along a straight line. If the acceleration is at an angle to the direction of motion, the object will turn. At the same time, it might speed up, slow down, or not change speed at all.

Motion is not always along a straight line.
Acceleration 2 Changing Direction Motion is not always along a straight line. If the acceleration is at an angle to the direction of motion, the object will turn. At the same time, it might speed up, slow down, or not change speed at all. Click image to view movie.

Calculating Acceleration
2 Calculating Acceleration If an object is moving in a straight line, its acceleration can be calculated using this equation. In SI units, acceleration has units of meters per second squared (m/s2).

Positive and Negative Acceleration
2 Positive and Negative Acceleration When you speed up, your final speed always will be greater than your initial speed. So subtracting your initial speed from your final speed gives a positive number. As a result, your acceleration is positive when you are speeding up.

Positive and Negative Acceleration
2 Positive and Negative Acceleration When your final speed is less than your initial speed, your acceleration is negative. Therefore, your acceleration is negative when you slow down.

Graphing Accelerated Motion
Acceleration 2 Graphing Accelerated Motion The motion of an object that is accelerating can be shown with a graph. For this type of graph, speed is plotted on the vertical axis and time on the horizontal axis.

Graphing Accelerated Motion
Acceleration 2 Graphing Accelerated Motion An object that is speeding up will have a line on a speed-time graph that slopes upward. An object that is slowing down will have a line on a speed-time graph that slopes downward. A horizontal line on the speed-time graph represents an acceleration of zero or constant speed.

Section Check 2 Question 1 A change in velocity divided by the time it takes for the change to occur equals the object’s _______.

Section Check 2 Answer The answer is acceleration. Remember that, like velocity, acceleration has a direction. A car that takes a turn has changed its acceleration, even if nothing else changes.

Section Check 2 Question 2 Imagine yourself driving a car down an empty stretch of road. How many ways could you change your acceleration?

Section Check 2 Answer You could step on the gas; you could also step on the brake; you could turn the wheel, or do any combination of these.

Question 3 2 What is happening at point C in this speed-time graph?
Section Check 2 Question 3 What is happening at point C in this speed-time graph?

A. the object is speeding up B. the object is slowing down
Section Check 2 A. the object is speeding up B. the object is slowing down C. the object is at rest D. the object is gone

Section Check 2 Answer The answer is B. When the line falls, the object is slowing down.

Momentum 3 Mass and Inertia The mass of an object is the amount of matter in the object. In SI units, the unit for mass is the kilogram. The weight of an object is related to the object's mass.

Momentum 3 Mass and Inertia Objects with more mass weigh more than objects with less mass. However, the size of an object is not the same as the mass of the object.

Momentum 3 Mass and Inertia The more mass an object has, the harder it is to start it moving, slow it down, speed it up, or turn it. This tendency of an object to resist a change in its motion is called inertia. Objects with more mass have more inertia.

Momentum is usually symbolized by p.
3 Momentum The momentum of an object is a measure of how hard it is to stop the object, and it depends on the object's mass and velocity. Momentum is usually symbolized by p.

Momentum 3 Momentum Mass is measured in kilograms and velocity has units of meters per second, so momentum has units of kilograms multiplied by meters per second (kg . m/s). Momentum has a direction that is the same as the direction of the velocity.

Conservation of Momentum
3 Conservation of Momentum According to the law of conservation of momentum, the total momentum of objects that collide is the same before and after the collision. This is true for the collisions of billiard balls, as well as for collisions of atoms, cars, football players, or any other matter.

Using Momentum Conservation
3 Using Momentum Conservation There are many ways that collisions can occur. Sometimes, the objects that collide will bounce off of each other. In other collisions, objects will stick to each other after the collisions. In both of these types of collisions, the law of conservation of momentum enables the speeds of the objects after the collisions to be calculated.

Imagine being on skates when someone throws a backpack to you.
Momentum 3 Sticking Together Imagine being on skates when someone throws a backpack to you. Before the student on skates and the backpack collide, she is not moving.

Momentum 3 Sticking Together

Supposed a 2-kg backpack is tossed at a speed of 5 m/s.
Momentum 3 Sticking Together Supposed a 2-kg backpack is tossed at a speed of 5 m/s. Your mass is 48 kg, and initially you are at rest. Then the total initial momentum is

You can use the equation for momentum to find the final velocity.
3 Sticking Together After the collision, the total momentum remains the same, and only one object is moving. You can use the equation for momentum to find the final velocity.

Colliding and Bouncing Off
Momentum 3 Colliding and Bouncing Off Supposed two identical objects moving with the same speed collide head on and bounce off. Before the collision, the momentum of each object is the same, but in opposite direction. So the total momentum before the collision is zero. Click image to view movie.

Colliding and Bouncing Off
Momentum 3 Colliding and Bouncing Off If momentum is conserved, the total momentum after the collision must be zero also. This means that the two objects must move in opposite directions with the same speed after the collision.

Section Check 3 Question 1 An object’s momentum can be increased either by increasing its _______ or its _______.

Section Check 3 Answer The answer is mass or velocity. A thrown baseball is harder to stop than a thrown ping-pong ball. At the same time, a baseball thrown by a professional pitcher is harder to stop than the same baseball lobbed by a fan.

Question 2 Answer 3 Explain the law of conservation of momentum.
Section Check 3 Question 2 Explain the law of conservation of momentum. Answer This law says that the total momentum of objects in collision is always the same after the collision as it was before the collision.

Section Check 3 Question 3 Two objects of the same mass are moving directly toward each other at the same speed. What is the total momentum of the two objects? Answer The total momentum is zero. This will be the same after the collision as well.

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