A professional race-car driver buys a car that can accelerate at 5.3 m/s 2 . The

Question

A professional race-car driver buys a car that can accelerate at 5.3 m/s 2 . The racer decides to race against another driver in a souped-up stock car. Both start from rest, but the stock-car driver leaves 1.4 s before the driver of the sports car. The stock car moves with a constant acceleration of +3.7 m/s a) Find the time it takes the sports-car driver to overtake the stock-car driver. Answer in units of s. b) Find the distance the two drivers travel before they are side by side. Answer in units of m. c) Find the velocity of the race car when the two drivers are side by side. Answer in units of m/s. d) Find the velocity of the stock car when the two drivers are side by side. Answer in units of m/s.

Explanation / Answer

just for help: (a) Let the sport car catches the stock car in t sec =>the distance covered by stock car in t-1 sec = the distance covered by sports car in t sec =>By s = ut + 1/2at^2 =>s(stock) = 0 + 1/2 x 3.6 x (t-1)^2 ------------(i) =>s (sport) = 0 + 1/2 x 5.9 x t^2 ----------------(ii) =>3.6t^2 - 7.2t + 3.6 = 5.9t^2 =>2.3t^2 + 7.2t - 3.6 = 0 =>t = [-7.2 +/- sqrt{(7.2)^2 - 4 x 2.3 x (-3.6)}]/[2 x 2.3] =>t = [-7.2 +/- 9.2]/4.6 =>t = 0.43 sec (b) By (ii):- =>s = 1/2 x 5.9 x (0.43)^2 =>s = 0.55 m (c) By v^2 = u^2 + 2as =>v = sqrt[2as] {as u =0 for both} =>v(sport) = sqrt[2 x 5.9 x 0.55] = 2.55 m/s =>v(stock) = sqrt[2 x 3.6 x 0.55] = 1.99 m/s

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