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2. A runner starts from rest toward the finish line 100.0m ahead of her, accelerating at 2.00 m/s?. How long does it take her to reach the finish line? If she had a running start of 1.00 m/s, how long would it take her to reach the finish line?

2. A runner starts from rest toward the finish line 100.0m ahead of her, accelerating at 2.00 m/s?. How long does it take her to reach the finish line? If she had a running start of 1.00 m/s, how long would it take her to reach the finish line?

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Physics Mechanics Problems #### Problem 2: A runner starts from rest toward the finish line 100.0 meters ahead of her, accelerating at \(2.00 \, \text{m/s}^2\). How long does it take her to reach the finish line? If she had a running start of \(1.00 \, \text{m/s}\), how long would it take her to reach the finish line? #### Problem 3: A race car starts from a dead-stop to reach the end of a 1.00 kilometer road in 12.5 seconds. What was the car’s acceleration and final velocity reaching the end of the road? #### Problem 4: An initially stationary rocket accelerates at \(5.75 \, \text{m/s}^2\) down a 12.0 kilometer path with no headwind or tailwind. What is its final velocity? How long did it take to travel the 12.0 km path? --- ### Solutions and Explanations **Problem 2 Solution:** To find the time taken for the runner to reach the finish line, use the kinematic equation: \[ s = ut + \frac{1}{2}at^2 \] Where: - \( s = 100.0 \, \text{m} \) - \( u = 0 \, \text{m/s} \) (initial velocity when starting from rest) - \( a = 2.00 \, \text{m/s}^2 \) - \( t \) is the time \[ 100 = 0 \cdot t + \frac{1}{2} \cdot 2.00 \cdot t^2 \] \[ 100 = t^2 \] \[ t = \sqrt{100} \] \[ t = 10 \, \text{s} \] With a running start of \(1.00 \, \text{m/s}\), use the same equation but consider the initial velocity: \[ s = ut + \frac{1}{2}at^2 \] Where: - \( s = 100.0 \, \text{m} \) - \( u = 1.00 \, \text{m/s} \) - \( a = 2.00 \, \text{m/s}^2 \) - \( t \) is
Transcribed Image Text:### Physics Mechanics Problems #### Problem 2: A runner starts from rest toward the finish line 100.0 meters ahead of her, accelerating at \(2.00 \, \text{m/s}^2\). How long does it take her to reach the finish line? If she had a running start of \(1.00 \, \text{m/s}\), how long would it take her to reach the finish line? #### Problem 3: A race car starts from a dead-stop to reach the end of a 1.00 kilometer road in 12.5 seconds. What was the car’s acceleration and final velocity reaching the end of the road? #### Problem 4: An initially stationary rocket accelerates at \(5.75 \, \text{m/s}^2\) down a 12.0 kilometer path with no headwind or tailwind. What is its final velocity? How long did it take to travel the 12.0 km path? --- ### Solutions and Explanations **Problem 2 Solution:** To find the time taken for the runner to reach the finish line, use the kinematic equation: \[ s = ut + \frac{1}{2}at^2 \] Where: - \( s = 100.0 \, \text{m} \) - \( u = 0 \, \text{m/s} \) (initial velocity when starting from rest) - \( a = 2.00 \, \text{m/s}^2 \) - \( t \) is the time \[ 100 = 0 \cdot t + \frac{1}{2} \cdot 2.00 \cdot t^2 \] \[ 100 = t^2 \] \[ t = \sqrt{100} \] \[ t = 10 \, \text{s} \] With a running start of \(1.00 \, \text{m/s}\), use the same equation but consider the initial velocity: \[ s = ut + \frac{1}{2}at^2 \] Where: - \( s = 100.0 \, \text{m} \) - \( u = 1.00 \, \text{m/s} \) - \( a = 2.00 \, \text{m/s}^2 \) - \( t \) is
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