Please help me with the set up and solutions (algebra based physics) An automobi

Question

Please help me with the set up and solutions (algebra based physics)

An automobile and a truck start from rest at the same instant, with the automobile initially at some distance behind the truck. The truck has a constant acceleration of 2.01m/s2, and the automobile an acceleration of 3.47m/s2. The automobile overtakes the truck after the truck has moved a distance of 45.0m 1)How much time does it take the automobile to overtake the truck? 2)How far was the automobile behind the truck initially? 3)What is the speed of the truck when they are abreast? 4)What is the speed of the automobile when they are abreast?

Explanation / Answer

(1) Initial velocities of both automobile and truck are equal to zero since they start from rest. Let Time taken to overtake = t Distance traveled by truck = 45                ( 1/2) a2 * t^2 = 45                0.5 * 2.01 * t^2 = 45                                    t = 6.69 s (2) Let d = Initial distance between automobile and truck Distance traveled by automobile = Distance traveled by truck + d (1/2) a1 t^2 = 45 + d 0.5 * 3.47 * 6.69^2 = 45 + d d = 32.69 m (3) Speed of the truck, v = a2 * t                                  = 2.01 * 6.69                                  = 13.45 m/s (4) Speed of the automobile, v = a1 * t                                           = 3.47 * 6.69                                           = 23.21 m/s

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