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# q1s - Physics 2211 Spring 2008 Quiz#1 Solutions Unless...

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Physics 2211 Quiz #1 Solutions Spring 2008 Unless otherwise directed, all springs, cords, and pulleys are ideal, and drag should be neglected. I . (16 points) A car is travelling in a straight line with velocity + v 0 . At time t = 0, it begins to accelerate at a = + k t , where k is a positive constant. Through what distance does the car travel between times t = 0 and t = T ? Express this distance in terms of any or all of v 0 , k , T , and physical or mathematical constants. . . . . . . . . . . . . . . . . . . . . . . . The acceleration is the time-derivative of the velocity, so a = dv/dt v = Z a dt = Z kt 1 / 2 dt = k t 3 / 2 3 / 2 + C where C is an integration constant. At time t = 0, the velocity is v 0 , so v 0 = 2 3 k 0 3 / 2 · + C C = v 0 so v = 2 3 kt 3 / 2 + v 0 Since the velocity is the time-derivative of the position, the displacement will be the definite integral of the velocity over time. v = dx/dt Δ x = Z t 2 t 1 v dt = Z T 0 2 3 kt 3 / 2 + v 0 · dt = 2 3 k t 5 / 2 5 / 2 + v 0 t fl fl fl fl T 0 So Δ x = 4 15 k T 5 / 2 + v 0 T Quiz #1 Solutions Page 1 of 5

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II . (16 points) You are motorcycling home, when you find your way blocked by a swollen stream. At that instant, you are directly north of your home, and a distance D away, as illustrated. You travel a distance a along the stream, in a direction θ south of east, to a bridge. How far from your home is the bridge, in terms of any or all of D , a , θ , and physical or mathematical constants? (The bridge has negligible length, so it does not matter which side you are on.) . . . . . . . . . . . . . . . . . . . . . . . Let the vector ~ D point from the starting position to home. Let the vector ~a point from the starting position to the bridge. Let the vector ~ b point from the bridge to home. Then ~a + ~ b = ~ D .
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q1s - Physics 2211 Spring 2008 Quiz#1 Solutions Unless...

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