A motor car travelling at the rate of 40 km/hr is stopped by its brakes in 4 seconds. How long will it go from the point at which the brakes are first applied?

Category: QuestionsA motor car travelling at the rate of 40 km/hr is stopped by its brakes in 4 seconds. How long will it go from the point at which the brakes are first applied?
Editor">Editor Staff asked 11 months ago

A motor car travelling at the rate of 40 km/hr is stopped by its brakes in 4 seconds. How long will it go from the point at which the brakes are first applied?
 
(a) 22m
 
(b) 22(2/9)m
 
(c) 22(1/9)m
 
(d) 22(4/9)m
 
This question was addressed to me in an international level competition.
 
This interesting question is from Calculus Application topic in section Application of Calculus of Mathematics – Class 12
NCERT Solutions for Subject Clas 12 Math Select the correct answer from above options 
Interview Questions and Answers, Database Interview Questions and Answers for Freshers and Experience

1 Answers
Editor">Editor Staff answered 11 months ago

Correct option is (b) 22(2/9)m
 
The best I can explain: Let f be the uniform retardation in m/sec^2 to the motion of the motor car due to application of brakes.
 
By question, the car is stopped by its brakes in 4 seconds, hence, the final velocity of the car after 4 seconds = 0.
 
Therefore, using the formula v = u – ft we get,
 
0 = ((40*1000)/(60*60) – f(4))  [Since u = initial velocity of the motor car = 40 km/hr = (40*1000)/(60*60) m/sec]
 
Or f = 25/9
 
Let the car go through a distance s m from the point at which the brakes are first applied.
 
Then using the formula s = ut – 1/2(ft^2) we get,
 
s = ((40*1000)/(60*60))*4 – 1/2(25/9)(4*4)
 
= 200/9
 
= 22(2/9)
 
Therefore, the required distance described by the car = 22(2/9)m.