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Unformatted text preview: 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 . 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 , k , T , and physical or mathematical constants. . . . . . . . . . . . . . . . . . . . . . . . The acceleration is the time-derivative of the velocity, so a = dv/dt v = Z adt = 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 , so v = 2 3 k 3 / 2 + C C = v so v = 2 3 kt 3 / 2 + v 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 x = Z t 2 t 1 v dt = Z T 2 3 kt 3 / 2 + v dt = 2 3 k t 5 / 2 5 / 2 + v t fl fl fl fl T So x = 4 15 k T 5 / 2 + v T Quiz #1 Solutions Page 1 of 5 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 south of east, to a bridge. How far from your home is the bridge, in terms of any or all of D , a , , and physical or mathematical constants? (The bridge has negligible length, so it does not matter which side you are on.) . . . . . . . . . . . . . . . . . . . . . . ....
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This note was uploaded on 06/17/2008 for the course PHYSICS 2211 taught by Professor Uzer during the Spring '08 term at Georgia Institute of Technology.
- Spring '08