Physics
Use the hockey puck's position-time graph to determine the time when the puck was 10.0 m beyond the origin.
0.5 s
Use the position-time graph to determine how far the hockey puck moved between 0.0 s and 5.0 s.
100 m
Use the position-time graph for the hockey puck to determine how much time it took for the puck to go from 40 m beyond the origin to 80 m beyond the origin.
2.0 s
A car travels north along a straight highway at an average speed of 85 km/h. After driving 2.0 km, the car passes a gas station and continues along the highway. What is the car's position relative to the start of its trip 0.25 h after it passes the gas station?
23 km
How does a motion diagram represent an object's motion?
A motion diagram shows the positions of a moving object at equal time intervals
Describe the difference between a vector and a scalar.
A vector has both magnitude and direction and a scalar has only magnitude.
Rank the position-time graphs according to the average speed, from greatest average speed to least average speed. Specifically indicate any ties.
A, B, C = D
How is an object's velocity related to its position?
An object's velocity is the rate of change in its position.
Explain the meaning of a position-time graph slope that is upward or downward, and above or below the x-axis.
An upward slope above the x-axis means the velocity is positive, and the object is moving away from the origin. An upward slope below the x-axis means the velocity is positive, and the object is moving toward the origin. A downward slope above the x-axis means the velocity is negative, and the object is moving toward the origin. A downward slope below the x-axis means the velocity is negative, and the object is moving away from the origin.
In solving a physics problem, why is it important to create pictorial and physical models before trying to solve an equation?
Answers will vary. Drawing the models helps you organize the problem situation. It is difficult to write the proper equation if you don't have a clear picture of how things are situated and/or moving. Also, you choose the coordinate system in this step, and this is essential in making sure you use the proper signs on the quantities you will substitute into the equation later.
Explain how average speed and average velocity are related to each other for an object in uniform motion.
Average speed is the absolute value of the average velocity if an object is in uniform motion.
Explain In the graph in Figure 19, the graph for both joggers starts at the coordinates (0,0). Explain what this means in terms of position.
Both joggers started at the same coordinates (0,0) or at the same position.
absolute value
magnitude of a number, regardless of sign
position-time graph
a graph that can be used to determine an object's velocity and position, as well as where and when two objects meet, made by plotting the time data on a horizontal axis and the position data on a vertical axis
1. ANALYZE AND SKETCH THE PROBLEM Choose a coordinate system with the origin at A
KNOWNS ̶v = 18 m/s east xi = 46 m east t = 2.8 s UNKNOWN x = ?
Describe in a few short sentences how plotting the motion of multiple objects on a position-time graph can be useful.
Sample answer: Plotting the motion of multiple objects on a position-time graph allows you to easily compare the positions of the objects at various times. You can easily see if the two objects will be at the same position at the same time.
Explain how positive and negative positions are determined.
Positive and negative positions are determined by the observer. (The observer defines a reference point, or a zero point, and defines which direction is positive and which direction is negative. The positive and negative directions must be opposite of each other.)
Summarize information about the many kinds of motion in three or four statements.
Sample answers: There are many types of motion, such as straight-line, curved, and spiral. Some types of motion are more complicated than others. The description of motion is a description of place and time.
2. SOLVE FOR THE UNKNOWN Question 1: Examine the graph to find the intersection of the lines representing the motions of the two runners. Question 2: Examine the graph to determine the position when the lines representing the motion of the runners intersect.
Runner B passes runner A about 100 m beyond the origin, 20 s after runner A has passed the origin.
Summarize how a coordinate system is used to diagram motion.
Sample answer: A coordinate system gives the location of the zero point of the variable, or where measurement begins for defining the motion of an object, and it defines the direction in which the values of the variable increase.
Compare and contrast a motion diagram and a particle model
Sample answer: A motion diagram is a series of images showing the positions of a moving object at equal time intervals. In a motion diagram the entire object is shown. In a particle diagram, a series of images showing the positions of a moving object at equal time intervals is also shown, but a single point represents the object.
Summarize the information about finding positions.
Sample answer: A position-time graph is a plot of an object's position at equal time intervals. It can be used to estimate the time or position of the object in motion. The graph can also be used to determine an object's instantaneous position.
Describe how you would model the motion of the hiker at the beginning of this module.
Student answers will vary. Student descriptions should be accurate and well thought out.
Draw a motion diagram for an object. Add the particle model diagram below the motion diagram. Add a coordinate system for the motion diagram below the particle model diagram. The starting point of the object should be the zero point
The diagram should look similar to the diagram in Figure 6 in the textbook. The object should start at the origin. The dots in the particle diagram should be evenly spaced to represent equal time intervals. The coordinate system should have evenly spaced numbers on a number line.
Describe what the direction and length of a displacement arrow indicate.
The direction of the arrow points from the origin to the object's position. The length represents the distance from the origin to the object's position.
Explain what the intersection of two lines on a position-time graph means.
The intersection of two lines on a position-time graph tells you when objects have the same position.
Describe differences in the average velocities shown on the graph for objects A and B. Describe differences in the average velocities shown on the graph for objects C and D.
The magnitude of the average velocity of A is greater than that of B, but the average velocity of A is negative, and the average velocity of B is positive. The magnitudes of the average velocities of C and D are equal, but the average velocity of D is positive, and the average velocity of C is negative.
Describe how the picture in Figure 1 would be different if the train were sitting still
The train would not be blurred because the train would not be in motion
Summarize the information about velocity and speed using a few sentences.
When you compare the slopes of multiple objects on a position-time graph, you can determine which of the objects is moving faster or slower than the other object. The absolute value of the slope on a position-time graph describes the object's average speed.
intersection
a point where lines meet and cross
model
a representation of an idea, event, structure, or object to help people better understand it
motion diagram
a series of images showing the positions of a moving object at equal time intervals
particle model
a simplified version of a motion diagram in which the object or objects of interest are replaced with single points
coordinate system
a system used to describe motion that gives the location of the zero point of the variable and the direction in which the values of the variables increase
3. EVALUATE THE ANSWER a) Are the units correct? b) Does the direction make sense?
a) Position is measured in meters. b) The motorcyclist is traveling east the entire time.
You can indicate how far an object is from the origin of a coordinate system by drawing an _______ from the ________ to the point that represents the object. This arrow represents the object's ________ . In general, the is ________ the entire length of an object's path, even if the object moves in many directions.
arrow origin position distance
displacement
change in position having both magnitude and direction
time interval
difference between two times
position
distance and direction from the origin to the object
dimension
extension in a given direction; one dimension is along a straight line; three dimensions are height, width, and length
origin
point at which all variables in a coordinate system have the value zero
vector
quantity that has both magnitude and direction
scalar
quantity that is just a number without any direction
2. Define the term average speed.
the distance traveled divided by the time taken to travel that distance
A quantity that has both magnitude and direction is called a ________. You can represent a ________ with an arrow. The ________ of the arrow represents the magnitude. The ________ of the arrow represents the ________ of the vector. A quantity that is a number without direction is a ________.
vector vector length direction direction scalar
resultant
vector that represents the sum of two other vectors
List five methods you can use to describe motion.
words, data tables, pictures, position-time graphs, motion diagrams
2. SOLVE FOR THE UNKNOWN Use the equation for position.
x = ̶vt + xi = (18 m/s)(2.8 s) + 46 m = +96.4 m x = 96 m east
Identify what the lengths of velocity vectors mean
Lengths of velocity vectors indicate the speed of the object.
Explain how average velocity is different from velocity.
Average velocity is determined by dividing the difference in the final and initial velocities by the time interval. It does not take into account any changes in velocity during the time interval. Instantaneous velocity is the velocity of an object at a specific moment in time.
1. What is the difference between average velocity and instantaneous velocity?
Average velocity is the quotient of an object's change in position divided by the time interval during which the change occurred. Instantaneous velocity is the speed and direction of an object at a particular instant
instantaneous position
the position of an object at any particular instant
magnitude
the size of a quantity
Two students added a vector for a moving object's position at t = 2 s to a motion diagram. When they compared their diagrams, they found that their vectors did not point in the same direction. Explain.
A position vector goes from the origin to the object. When the origins are different, the position vectors are different. On the other hand, a displacement vector has nothing to do with the origin.
Rank the graphs in Figure 25 according to each object's initial position, from most positive position to most negative position. Specifically indicate any ties. Would your ranking be different if you ranked according to initial distance from the origin?
A, C, B, D. Yes; the ranking from greatest to least distance would be A, C, D, B.
Look at the diagram and graph shown in Figure 18. Do they describe the same motion? Explain. The time intervals in the particle model diagram are 2 s.
No, they don't describe the same motion. Although both objects are traveling in the positive direction, one is moving more quickly than the other. Students can cite a number of different specific examples from the graph and particle model to back this up. For example, the particle model shows a position of 2 m after 2 s, but the graph shows a position of 8 m after 2 s.
Describe a scenario that is not in the textbook in which photographs can be used to describe the motion of an object.
Sample answer: A series of photographs could be used to describe the motion of a horse running along a fence line.
Describe what a motion diagram is in your own words.
Sample answer: It is like a single image of multiple photos superimposed on top of each other. Stationary objects in the photograph are aligned. The motion of the object is obvious because the object is moving relative to the background.
Explain how an object can have a negative position in a coordinate system.
Sample answer: The object is located in the direction that is opposite the direction that is defined as the positive direction. For example, the object is located to the left of the origin, if right of the origin is defined as the positive direction.
Identify a coordinate system you could use to describe the motion of a girl swimming across a rectangular pool.
Sample answer: The position direction could be along the length of the pool. The origin could be at one of the short sides of the pool.Sample answer: The position direction could be along the length of the pool. The origin could be at one of the short sides of the pool.
Two cars are traveling along a straight road, as shown in Figure 26. They pass each other at point B and then continue in opposite directions. The orange car travels for 0.25 h from point B to point C at a constant velocity of 32 km/h east. The blue car travels for 0.25 h from point B to point D at a constant velocity of 48 km/h west. How far has each car traveled from point B? What is the position of each car relative to the origin, point A?
The orange car has traveled 8 km east of point B. The blue car has traveled 12 km west of point B. The orange car's position is 14 km east of the origin. The blue car's position is 6 km west of the origin.
Draw a particle model motion diagram corresponding to the motion diagram in Figure 5 for a flying bird. What point on the bird did you choose to represent the bird?
The point should be close to the center of the bird. The equal distances between the dots indicate that the bird was flying at a constant speed.
Draw a particle model motion diagram corresponding to the motion diagram in Figure 4 for a car coming to a stop at a stop sign. What point on the car did you use to represent the car?
The point should be close to the center of the car. As the car slowed down as it moved to the left, the distance it traveled during each equal time interval became less and less.
Using the particle model motion diagram in Figure 16 of a baby crawling across a kitchen floor, plot a position-time graph to represent the baby's motion. The time interval between successive dots on the diagram is 1 s.
The straight line formed by the dots indicated the baby crawled at a constant speed. The positive slope of the line of dots shows that the baby was crawling in the positive direction away from the origin.
Identify two factors you must know in order to describe the motion of an object along a straight line.
You must know where an object is located at different times and when it is at each position
distance
entire length of an object's path