1. A straight track 180 m long is used torace small carts (which are big enough

Question

1.     A straight track 180 m long is used torace small carts (which are big enough for just one person to sitin). During the race, a particular cart travels the first 50m with a constant speed of 13.39 m/s. For the next 43 m ofthe track the cart experiences some mechanical difficulties andslows down at a uniform rate of 0.38 m/s2. Then,for the next 17 m of the race, the driver travels at a constantspeed. At this point, and for the final 70 m of the race thedriver steps on the gas pedal and accelerates at a uniform rate of0.74 m/s2. Determine the total time that it tookfor the cart to travel the 180 m distance and cross the finishline.

Explanation / Answer

First 50 m : ------------ Distance S = 50 m speed v = 13.39 m / s time taken t = S / v                   = 3.734 s next 43 m : ----------- Accleration a = -0.38 m / s ^ 2 distance S ' = 43 m initial velocity u ' = 13.39 m / s from the relation v ' ^ 2 - u ' ^ 2 = 2aS final velocity v ' = [ u ' ^ 2 + 2aS ]                       = 12.108 m / s timetaken t ' = ( v - u ) / a                    = 3.372 s next 17 m : ---------- speed v " = 12.108 m / s distance S " = 17 m time t " = S " / v "            = 1.404 s next 70 m : ---------- accleration a " = 0.74 m / s ^ 2 distance s = 70 m initial velocity U = 12.108 m / s final velocity V = [ U ^ 2 + 2a"s ]                        = 15.817 m / s time T = ( V - U ) / a"           =5.013 s total time = 3.734+3.372+1.404+5.013                = 13.523 s

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