An automobile and a truck start from rest at the same instant, withthe automobil

Question

An automobile and a truck start from rest at the same instant, withthe automobile initially at some distance behind the truck. Thetruck has a constant acceleration of 2.40m/s2, and the automobile an acceleration of 3.50 m/s2. The automobile overtakes thetruck after the truck has moved 54.0 m. (a) How much time does it take the automobileto overtake the truck?
1 s

(b) How far was the automobile behind the truck initially?
2 m

(c) What is the speed of each when they are abreast?
automobile:
3 m/s
truckL
4 m/s
(a) How much time does it take the automobileto overtake the truck?
1 s

(b) How far was the automobile behind the truck initially?
2 m

(c) What is the speed of each when they are abreast?
automobile:
3 m/s
truckL
4 m/s

Explanation / Answer

(a) Time taken to overtake is                   54.0m = (1/2)(3.50m/s2)(t)2                         t = 5.55s (b) Total distance traveled by the truck in the time 5.55sis               S = (1/2)(2.40m/s2)(5.55s)2                  = 37.03m Total distance behind initially = 54.0m - 37.03m =16.97m (c) FInal speed of the truck is v = u + at                                           = 0 + (2.40 m/s2)(5.55s) =13.32m/s Final speed of the automobile is v = u + at                                                    = 0 + (3.50 m/s2)(5.55s) =19.425 m/s                  = 37.03m Total distance behind initially = 54.0m - 37.03m =16.97m (c) FInal speed of the truck is v = u + at                                           = 0 + (2.40 m/s2)(5.55s) =13.32m/s Final speed of the automobile is v = u + at                                                    = 0 + (3.50 m/s2)(5.55s) =19.425 m/s

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