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Unformatted text preview: valdez (vv689) Sample Final florin (58140) 1 This printout should have 27 questions. Multiplechoice questions may continue on the next column or page find all choices before answering. 001 10.0 points A train pulls away from a station with a con stant acceleration of 0 . 5 m / s 2 . A passenger arrives at a position on the track 5 s after the end of the train left that position. What is the slowest constant speed at which she can run and catch the train? Correct answer: 5 m / s. Explanation: Let : x = 0 m , end of train position v t = 0 m / s , a t = 0 . 5 m / s 2 , and t = 5 s . After time t the train has traveled a dis tance of x t = x + v t t + 1 2 a t t 2 = 1 2 a t t 2 and the passenger a distance of x p = x + v p ( t t ) = v p ( t t ) . When the passenger overtakes the train, x t = x p v p ( t t ) = 1 2 a t t 2 v p = a t t 2 2 ( t t ) . To minimize v p , d dt bracketleftbigg a t t 2 2 ( t t ) bracketrightbigg = 0 4 ( t t ) a t t 2 a t t 2 4 ( t t ) 2 = 0 2 ( t t ) t = 0 t 2 t = 0 t = 2 t = 2 (5 s) = 10 s , so v p = a t t 2 2 ( t t ) = a t (2 t ) 2 2 t = 2 a t t = 2 (0 . 5 m / s 2 ) (5 s) = 5 m / s . 4 8 12 16 5 10 15 20 25 30 35 40 45 50 x (m) t (s) t Train Passenger The trains velocity at this time is v t = a t t = 2 a t t = 2 (0 . 5 m / s 2 ) (5 s) = 5 m / s . The dashed line (representing the passen gers minimum constant velocity) is tangent to the trains acceleration curve, illustrating the fact that the velocities are equal at the passengers minimum speed. 002 10.0 points Two bodies are falling with negligible air resis tance, side by side, above a horizontal plane. If one of the bodies is given an additional horizontal acceleration during its descent, it 1. follows a straight line path along the re sultant acceleration vector. 2. has the vertical component of its acceler ation altered. 3. strikes the plane at the same time as the other body. correct valdez (vv689) Sample Final florin (58140) 2 4. has the vertical component of its velocity altered. 5. follows a hyperbolic path. Explanation: Because a horizontal acceleration does not change the vertical velocity of an object, the two bodies strike the plane at the same time. 003 10.0 points A man stands in an elevator in the universitys administration building and is accelerating upwards. (During peak hours, this does not happen very often.) Elevator Cable Choose the correct free body diagram for the man, where F i,j is the force on the object i , from the object j . 1. F elevator, cable F man, elevator 2. F man, acceleration 3. F man, floor F elevator, cable F man, earth 4. F F man, floor man, earth correct 5....
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