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Question

A driver, having a definite reaction time, is capable of stopping over a distance of 30 m on seeing a red traffic light when speed of the car is 72 km/hr and over a distance of 10 m when the speed is 36 km/hr. Assuming that his reaction time and the acceleration of the car remain the same in all cases, find the distance over which he can stop the car when he is going at 54 km/hr.

A
11.75 m
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B
13.75 m
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C
15.75 m
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D
18.75 m
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Solution

The correct option is D 18.75 m
Let the reaction time of driver be t
So, the distance covered before application of brake =20t m
For the first case, speed of the car is 72 km/hr=20 m/s
So, we have
v2u2=2as 02202=2a(3020t)...(i)
Similarly, in the second case, speed of the car is 36 km/hr=10 m/s
0102=2a(1010t)...(ii)
On solving (i) and (ii) we get
400100=2a(3020t)2a(1010t)
4=3020t1010t
or, 4040t=3020t 20t=10
or, t=0.5 sec
and, putting the value of t in any equation we get a=10 m/s2
So, in the third case, let the stopping distance be s
Thus, speed of the car is 54 km/hr=15 m/s
02152=2×10(s15×0.5)
225=20(s7.5) 11.25=s7.5
s=18.75 m

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