The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m,

Question

The minimum stopping distance for a car traveling at a speed of 30 m/s is 60 m, including the distance traveled during the driver's reaction time of 0.640

What is the minimum stopping distance for the same car traveling at a speed of 32.0 ?


I would like the formula, and why you used that formula. And then the answer please.
Thanks!

Explanation / Answer

To solve this question we need to find the rate of acceleration of the car. Speed of car =30m/sec Distance = 60 m Reaction time = 0.64 Let the acceleration be a Now we first remove the distance which is traveled by user while the driver pushes the break Till the driver pushes the break the speed is 30 m/sec and time =0.64 Distance = .64*30 = 19.2 m So the distance at which the car come to rest from 30 to 0 is 60-19.2 = 40.8 V^2 = u^2 +2as => 0 = 30^2 + 2*40.8*a =>a = 11.03m/s^2 Now for car travelling at 32 m/sec Distance traveled till driver reacts = .64*32 = 20.48m Now for the rest it accelerates at -11.03m/s^2 Let this distance be d v^2 = u^2 +2as => -32^2 = -2*11.03*d =>d = 512/11.03 =46.42m Total distance = 46.42 + 20.48 = 66.9m

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