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Chapter_2_homework_solutions_Physics_1301_Spring_2011

# Chapter_2_homework_solutions_Physics_1301_Spring_2011 - 20...

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20. Picture the Problem : You travel in a straight line at two different speeds during the specified time interval. Strategy: Determine the average speed by first calculating the total distance traveled and then dividing it by the total time elapsed. Solution: 1. (a) Because the time intervals are the same, you spend equal times at 20 m/s and 30 m/s, and your average speed will be equal to 25.0 m/s. 2. (b) Divide the total distance by the time elapsed: ( 29 ( 29 ( 29 ( 29 1 1 2 2 av 1 2 av 20.0 m/s 10.0 min 60 s 30.0 m/s 600 s 600 600 s 25.0 m/s s t s t s t t s × + + = = + ∆ + = Insight: The average speed is a weighted average according to how much time you spend traveling at each speed. 25. Picture the Problem : The given position function indicates the particle begins traveling in the positive direction but is accelerating in the negative direction. Strategy: Create the x - versus - t plot using a spreadsheet, or calculate individual values by hand and sketch the curve using graph paper. Use the known x and t information to determine the average speed and velocity. Solution: 1. (a) Use a spreadsheet to create the plot shown at right: 2. (b) Find the average velocity from t = 0 to t = 1.0 s: ( 29 ( 29 ( 29 ( 29 [ ] av 2 2 av 6 m/s 1.0 s 2 m/s 1.0 s 0.0 m 1.0 s 4.0 m/s x v t v = + - - = = 3. (c) The average speed is the magnitude of the average velocity: av av 4.0 m/s s v = = Insight: Note that the average velocity over the first second of time is equal to the slope of a straight line

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