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1) Average speed is the total distance traveled divided by the time taken to cover the distance. We use the letters s for speed, d for distance, and t for time whence: s av = d/t. The SI units of speed are m/s. Usain Bolt traveled 100 m in 9.63 s. What was his average speed?

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2) A multi-exposure photograph is made in a totally dark room with a strobe and a camera with an open shutter. If you travel 40 miles in 2 hours your average speed is s av = 40 mi/2 h = 20 mi/h = 20 mph. Average speed tells you nothing about the details of the trip. What is happening to the speed of the blue ball?

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3) Instantaneous speed is equal to the average speed over a time interval that is very, very small. For practical purposes we need a time interval that is small enough that the average speed does not change very much if we use an even smaller time interval. Think of instantaneous speed as what a speedometer says. How does it work?

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4) Velocity is speed and direction. The magnitude of velocity is speed. Quantities that have both magnitude and direction are called vectors. Average velocity is displacement divided by time. v av = x/t. Displacement is a vector quantity whose magnitude is the straight-line distance from A to B and whose direction is the direction from A to B. Is the displacement vector ever longer than the distance traveled?

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5) Average acceleration is the change in velocity divided by the time it takes to make that change. We use the letters a for acceleration, v for velocity, and t for time whence: a av = v/ t. The SI units of acceleration are m/s 2. When you travel in a straight line at a constant speed your acceleration is zero. The falling ball accelerates!

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6) According to Aristotle, a heavy physics text should fall significantly faster than a crumpled piece of paper. According to Galileo, in a vacuum, the falling speeds of a cannonball and a feather should be equal. Astronauts conducted an ultramodern demonstration of this on the Moon where a hammer and a feather fell at the same rate. Why does the hammer fall faster on Earth?

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7) As Galileo let balls roll down steeper ramps he discovered the following rule: the acceleration in each case is constant. Constant acceleration means the speed changes by the same amount each second. In the case of free fall the acceleration due to gravity is about 9.8 m/s 2. We use the letter g for this acceleration and usually round it off whence: g = 10 m/s 2.

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8) If you throw a ball vertically upward with an initial speed of 20 m/s, one second later its instantaneous speed will be 10 m/s. As the ball continues to rise against gravity it continues to lose speed. It will reach its maximum height in 2 seconds. At that moment the instantaneous speed of the ball will be zero. Is the ball rising or falling?

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Exercise 58

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Exercise 60

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Exercise 62

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Exercise 64

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Exercise 66

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Exercise 68

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Exercise 70

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Exercise 72

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Exercise 74

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Exercise 76

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Exercise 80

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