41_Dynamics 11ed Manual - Engineering Mechanics - Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics Chapter 12 Problem 12-53 Two cars start from rest side by side and travel along a straight road. Car A accelerates at the rate aA for a time t1, and then maintains a constant speed. Car B accelerates at the rate aB until reaching a constant speed vB and then maintains this speed. Construct the a-t, v-t, and s-t graphs for each car until t = t2. What is the distance between the two cars when t = t2? aA = 4 Given: m t1 = 10 s 2 aB = 5 s m vB = 25 2 s m s t2 = 15 s Solution: Car A : 2 τ 1 = 0 , 0.01 t1 .. t1 a1 ( t ) = aA τ 2 = t1 , 1.01 t1 .. t2 a2 ( t ) = 0 s m 2 v1 ( t) = aA t v2 ( t) = v1 ( t1 ) s m s2 ( t) = t3 = Car B : s m vB s1 ( t) = s m ⎡ 1 a t 2 + a t ( t − t )⎤ 1 ⎢ A1 A1 1⎥ ⎣2 ⎦m aB 2 τ 3 = 0 , 0.01 t3 .. t3 a3 ( t ) = aB τ 4 = t3 , 1.01 t3 .. t2 s m a4 ( t ) = 0 v3 ( t) = aB t s m v4 ( t) = aB t3 s4 ( t) = s3 ( t) = 1 21 aB t m 2 s m ⎡ 1 a t 2 + a t ( t − t )⎤ 1 ⎢ B3 B3 3⎥ ⎣2 ⎦m Car A Car B 5 Acceleration in m/s^2 5 Acceleration in m/s^2 1 21 aA t m 2 () a 2( τ 2) a1 τ 1 0 0 10 20 () a 4( τ 4) a3 τ 3 0 0 τ1, τ2 5 10 τ3, τ4 Time in seconds Time in seconds 39 15 ...
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