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Ch2-HW2-solutions - louey(cal2859 Ch2-HW2 florin(56930 This...

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louey (cal2859) – Ch2-HW2 – florin – (56930) 1 This print-out should have 18 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001(part1of2)10.0points You’re driving on a straight road (in the + x direction) at a constant speed of 27 m / s. In 8 s, you speed up to 45 m / s to pass a truck. Assuming that your car speeds up at a con- stant rate (constant force by the road on the tires), what is your average x component of velocity v avg ,x during this maneuver? Correct answer: 36 m / s. Explanation: Since the car speeds up at a constant rate, we just need to consider the endpoints, when the car was traveling v i,x = 27 m / s and v f,x = 45 m / s . We calculate the average x component of ve- locity as follows: v avg ,x = v i,x + v f,x 2 = 27 m / s + 45 m / s 2 = 36 m / s . 002(part2of2)10.0points How far do you go during this maneuver? Correct answer: 288 m. Explanation: Again, the fact that the acceleration is con- stant simplifies things. We can just treat this situation as though we were actually moving at the average speed for the 8 s interval: Δ x = = v avg ,x Δ t = (36 m / s)(8 s) = 288 m . 003(part1of3)0.0points On a straight road (taken to be in the + x direction) you drive for an hour at v 1 ,x = 35 km / h , then quickly speed up to v 2 ,x = 90 km / h and drive for an additional two hours. How far do you go (Δ x )? Correct answer: 215 km. Explanation: To find the total distance traveled, we have to consider the two speeds separately: Δ x = v 1 ,x Δ t 1 + v 2 ,x Δ t 2 = (35 km / h)(1 h) + (90 km / h)(2 h) = 215 km . 004(part2of3)0.0points What is your average x component of velocity ( v avg ,x )? Correct answer: 71 . 6667 km / h. Explanation: We can’t simply take the arithmetic mean in this case, because the car did not accelerate at a constant rate between the initial and final speeds. Instead, we have to take a weighted average, considering the two speeds and how long the car spent at each speed: v avg ,x = v 1 ,x t 1 + v 2 ,x t 2 t 1 + t 2 = (35 km / h)(1 h) + (90 km / h)(2 h) 2 h + 1 h = 71 . 6667 km / h . 005(part3of3)0.0points
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louey (cal2859) – Ch2-HW2 – florin – (56930) 2 Is v avg ,x equal to the arithmetic average of your initial and final values of v x ? 1. No correct 2. Yes Explanation: As we can see, they are not equal: v arith ,x = 35 km / h + 90 km / h 2 = 62 . 5 km / h .
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