Arizona State University| PHY 121: Univ Physics I: Mechanics|Homework 1-1| Problem 3

Learning Goal:

To practice Problem-Solving Strategy 1.1 for motion diagram problems.
PROBLEM-SOLVING STRATEGY 1.1 Motion diagrams

MODEL: Determine whether it is appropriate to model the moving object as a particle. Make simplifying assumptions when interpreting the problem statement.

VISUALIZE: A complete motion diagram consists of:

  • The position of the object in each frame of the video, shown as a dot. Use five or six dots to make the motion clear but without overcrowding the picture. More complex motions may need more dots.
  • The average velocity vectors, found by connecting each dot in the motion diagram to the next with a vector arrow. There is one velocity vector linking each set of two position dots. Label the row of velocity vectors v⃗ .
  • The average acceleration vectors, found using Tactics Box 1.3. There is one acceleration vector linking each set of two velocity vectors. Each acceleration vector is drawn at the dot between the two velocity vectors it links. Use 0⃗  to indicate a point at which the acceleration is zero. Label the row of acceleration vectors a⃗ .

PROBLEM:

A car is traveling with constant velocity along a highway. The driver notices he is late for work, so he stomps down on the gas pedal and the car begins to speed up. The car has just achieved double its initial velocity when the driver spots a police officer behind him and applies the brakes. The car then slows down, coming to rest at a stoplight ahead. Draw a complete motion diagram for this situation.

Part A

The car’s motion can be divided into three different stages: its motion before the driver realizes he’s late, its motion after the driver hits the gas (but before he sees the police car), and its motion after the driver sees the police car. Which of the following simplifying assumptions is it reasonable to make in this problem?

A. During each of the three different stages of its motion, the car is moving with constant acceleration.
B. During each of the three different stages of its motion, the car is moving with constant velocity.
C. The highway is straight (i.e., there are no curves).
D. The highway is level (i.e., there are no hills or valleys).

Enter all the correct answers in alphabetical order without commas. For example, if statements C and D are correct, enter CD.

Part B

In the three diagrams shown to the left, the position of the car at five subsequent instants of time is represented by black dots, and the car’s average velocity is represented by green arrows. Which of these diagrams best describes the position and the velocity of the car before the driver notices he is late? 

The figure shows three motion diagrams. Diagram A shows equal segments. Diagram B shows lengthening segments. Diagram C shows shortening segments.
Part C
Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver hits the gas, but before he notices the police officer?
Part D
Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver notices the police officer?
Part E

Which of the diagrams shown below most accurately depicts the average acceleration vectors of the car during the events described in the problem introduction?

The figure shows three acceleration diagrams. Diagram A shows four equal forward segments followed by three equal backward segments. Diagram B shows two 0 vectors followed by two equal forward segments, followed by three equal backward segments. Diagram C shows two 0 vectors followed by five equal forward segments.

ANSWERS:

PART A

Answer: ACD

In addition to the assumptions listed above, in the rest of this problem assume that the car is moving in a straight line to the right.

PART B

Answer: A

PART C

Answer: B

PART D

Answer: C

PART E

Answer: B

You can now draw a complete motion diagram for the situation described in this problem. Your diagram should look like this:

The figure shows a motion diagram for a car. Before the driver hits the gas pedal, the diagram shows 0 acceleration and equal segments. Before the driver sees the police, the diagram shows a forward acceleration and lengthening segments. Before the car stops, the diagram shows a backward acceleration and shortening segments.

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