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valleyldp

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- Homework Statement
- STORY PROBLEM:

Sarah is speeding down the highway westward at 65 mph. She notices ahead that an accident has resulted in a pile-up in the middle of the road. She slams on her brakes 35 meters from the accident, causing her car to slow at a rate of 9.1 m/s^2. Andrew is traveling the other way on the same highway at 45 m/s eastward. He also notices the accident and begins to brake 20 meters from the accident. His car decelerates at 8.8 m/s^2. Assuming a damaged car will keep them home from work, which of the two people will be able to make it to work the next day?

STEPS TO SOLVE:

1. Draw a diagram to model the situation with relevant items labeled. Make sure you indicate which direction is east or west, and which of those you chose to be positive.

2. What are the signs for the following information as defined by your model? (Correct or not).

3. Construct a velocity versus time graph of both Sarah's and Andrew's motion in the same reference frame.

4. Write out the stopping time needed for each person indicated by the graph. (Correct sig figs and units required)

5. Use a kinematic equation to determine the distance needed for each person to stop. (Correct sig figs and units required)

6. Which personal will make it to work the next day?

- Relevant Equations
- Δx=v_iΔt+½a(Δt)^2

- Model attached below.
- Changed Sarah's 65 mph to m/s and got 29 m/s.

- Sarah's initial position is positive. Her initial velocity is negative. Her acceleration is positive; Andrew's initial position is negative. His initial velocity is positive. His acceleration is negative.
- Graph is attached below.
- Graph indicates a stopping time of 3.2 seconds for Sarah and 5.1 seconds for Andrew.
*(Two sig figs because measurements in initial problem were two sig figs.)* - Worked Out Equations (Δx=v_iΔt+½a(Δt)^2)
- Sarah
- Δx = unknown
- a = -9.1 m/s^2
- Initial Velocity = 29 m/s
- Δt = 3.2 seconds
**Answer: 46 meters**

- Andrew
- Δx = unknown
- a = -8.8 m/s^2
- Initial Velocity = 45 m/s
- Δt = 5.1 seconds
**Answer: 120 meters**

- Sarah
- Neither person will make it to work the next day because the required stopping distance is more than the given distances.

#### Attachments

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