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Chapter 2 Additional Examples 1. In getting ready to slam-dunk the ball, a basketball player starts from rest to a speed of 6m/s in 1.5s. Assuming constant acceleration, determine the distance he runs. Since we are assuming constant acceleration, we can use the kinematic equations. Since we know the initial and final velocities and the time we can determine the acceleration. v = v 0 + at = 0 + at

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Solving for the acceleration we have a = v t = 6 m / s 1.5 s = 4 m / s 2 Now that we have the acceleration we can find the distance. So we have x = x 0 + v 0 t + 1 2 at 2 = 0 + 0 + 1 2 at 2 = 1 2 (4 m / s 2 )(1.5 s ) 2 = 4.5 m
2. A car traveling at a constant speed of 30m/s when it passes a hidden police car at rest. When the car is 10m from the police car, the police car accelerates at 5m/s^2. How far does the police car travel before it reaches the car, which continues traveling at 30m/s? How fast is the police car moving when catches the car? x x 0 C = 10 m v 0 C = 30 m

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The equation of motion for the police car is x = x 0 P + v 0 P t + 1 2 a P t 2 = 0 + 0 + 1 2 a P t 2 = 1 2 a P t 2 The equation of motion for the car is x = x 0 C + v 0 C t + 1 2 a C t 2 = x 0 C + v 0 C t + 0 = x 0 C + v 0 C t Since we are taking the origin at the police car!
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