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Chapter 2: Q6. (page 41)
Can the velocity of an object be negative when its acceleration is positive? What about vice versa? If yes, give examples in each case.
Yes, the velocity of an object can be negative even its acceleration is positive.
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Consider the street pattern shown in Fig. 2–46. Each inter-section has a traffic signal, and the speed limit is 40 km/h. Suppose you are driving from the west at the speed limit. When you are 10.0 m from the first intersection, all the lights turn green. The lights are green for 13.0 s each. (a) Calculate the time needed to reach the third stoplight. Can you make it through all three lights without stopping? (b) Another car was stopped at the first light when all the lights turned green. It can accelerate at the rate ofto the speed limit. Can the second car make it through all three lights without stopping? By how many seconds would it make it, or not make it?
FIGURE 2-46Problem 65
A baseball is seen to pass upward by a window with a vertical speed of 14 m/s. If the ball was thrown by a person 18 m below on the street, (a) what was its initial speed, (b) what altitude did it reach, (c) when was it thrown, and (d) when does it reach the street again?
A car is behind a truck goingon the highway. The car’s driver looks for an opportunity to pass, guessing that his car can accelerate atand that he has to cover the 20-m length of the truck, plus 10-m extra space at the rear of the truck and 10 m more at the front of it. In the oncoming lane, he sees a car approaching, probably at the speed limit,(55 mph). He estimates that the car is about 500 m away. Should he attempt the pass? Give details.
In a putting game, the force with which a golfer strikes a ball is planned so that the ball will stop within some small distance of the cup, say 1.0 m long or short, in case the putt is missed. Accomplishing this from an uphill lie (that is, putting the ball downhill, see Fig. 2–47) is more difficult than from a downhill lie. Assume that on a particular green, the ball constantly decelerates atgoing downhill and atgoing uphill to see why. Suppose you have an uphill lie 7.0 m from the cup. Calculate the allowable range of initial velocities you may impart to the ball so that it stops in the range 1.0 m short to 1.0 m long of the cup. Do the same for a downhill lie 7.0 m from the cup. What, in your results, suggests that the downhill putt is more difficult?
FIGURE 2-47 Problem 70
A baseball pitcher throws a baseball with a speed of 43 m/s. Estimate the average acceleration of the ball during the throwing motion. In throwing the baseball, the pitcher accelerates it through a displacement of about 3.5 m, from behind the body to the point where it is released. (Fig. 2-37).
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