Chapter 4 review

    Quantitative problems
      Section 4.1
        Position versus time graph
      1. Answer the following questions based on the position versus time graph above.
        1. What is the average velocity over the whole 50 s interval shown?
        2. What is the maximum speed shown on the graph?
        3. What is the total distance traveled between t = 0 and t = 50 s?
        4. What is the final position at t = 50 s?
        5. How does the acceleration at t = 10 s compare with the acceleration at t = 30 s?

      2. A car traveling at 15 m/s in a straight line accelerates for 5 s with an acceleration of 2 m/s2. What is its final velocity?

      3. How long should Pete’s approach to his long jump attempt be if he wants to be at a speed of 9 m/s and can accelerate at 4 m/s2?

      4. Rachel is walking at 3 m/s when she walks into a glass door and stops in 0.05 s. What is her acceleration?

      5. Challenging A zebra is at rest 60 m away from a charging lion running at 17 m/s. If the zebra accelerates at 2 m/s2, will the lion catch it?

      6. A submarine begins ascending to the surface of the ocean. It experiences an overall acceleration of 1.7 m/s2 for the first 5 s. What is its velocity after 3.2 s?

      7. Easy What is the average acceleration of a cheetah that starts at rest and 3 s later is moving at a speed of 27 m/s? Is the acceleration greater or less than the acceleration of a $100,000 sports car that can go from 0 to 60 mph in 4 s?

      8. Easy Jane is riding her bicycle at 10 m/s when she begins to decelerate at 1.5 m/s2.
        1. How long will it take Jane to stop?
        2. How far will she have traveled in this time?

      1. At her most recent track race, Stella had an acceleration of 2.1 m/s2 during the first 3 s of the race. What was her velocity after 2 s?

      2. Medium A speeding car traveling at 35 m/s passes a stationary police car. At the moment the car passes, the police car starts accelerating in the same direction with an acceleration of 3 m/s2.
        1. How long does it take the police car to catch up with the speeder?
        2. What is the speed of the police car at the moment it catches up with the speeder?
        3. How far have both cars traveled when the police car catches up?
        4. Convert both car’s speeds to miles per hour. Is it likely the police car would actually catch the speeder? Explain your reasoning.

      3. Medium A motorcycle has a maximum acceleration of 3 m/s2 in either direction and a maximum speed of 25 m/s. How long does it take for the motorcycle to reach someone who is 1 km away?

      4. Medium A car travels 100 m while decelerating to 8 m/s in 5 s. What was its initial speed? What is the magnitude of the acceleration?

        5. ErgoBot data in “ticker tape” chart mode
      5. Medium When operated in “ticker tape” chart mode, moving the ErgoBot by hand will generate a chart with a dot plotted every 0.1 s.
        1. In the ticker tape chart above, where does the ErgoBot have positive acceleration?
        2. Where does it have negative acceleration?
        3. Explain what features in the chart you interpret as positive and negative acceleration.
        4. If the dots were spaced widely apart in the chart, then what could you infer about the speed of the ErgoBot?

      6. Medium Linda is out jogging at a constant speed of 3 m/s. She jogs past Maggie, who is stationary but immediately takes off on her bicycle to try and catch up to Linda. Maggie accelerates on her bicycle at 2 m/s2. How long does it take Maggie to catch Linda?

      7. Medium Vinny is on a motorcycle at rest, 200 m away from a ramp that jumps over a gully. Calculate the minimum constant acceleration Vinny must have to get to the ramp in 8 s before his pursuers catch up with him.

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