A driver having a definite reaction time is capable of stopping his car over a distance of 30 m on seeing a red traffic signal, when the speed of the car is 72 km/hr andover a distance of 10 m when the speed is 36 km/hr. Find the distance over which he can stop the car if it were running at a speed of 54 km/hr. Assume that his reaction time and the deceleration of the car remains same in all the three cases.

Explanation

If v is the maximum velocity attained,then during acceleration ie between A,B
`v^(2)-0^(2)=2xx5xxS_(1)impliesS_(1)=(v^(2))/(10)`
Also during retardation
`o^(2)-v^(2)=2xx10xxS_((2)impliesS_(2)(v^(2))/(20)`
`S=S_(1)+S_(2)implies1500=(v^(2))/(10)+(v^(2))/(20)=(3v^(2))/(20)` or
`v^(2)=(1500xx20)/(3)=10000` or v=100 `ms^(-1)`
`v=alphat_(1)impliest_(1)(100)/(5)=20sec`
`v=betat_(2)impliest_(2)=(100)/(10)`=10sec
Total time=20+10=30 sec.