Question

The range of headlights of a car is 25m find the limiting safety speed of the car if coefficient of friction between tyre of a car and the road is 0.4

Answer 1

Range of headlights is 25m so car should stop in 25m of distance when danger sensed
Therefore maximum de acceleration produces by force of friction will be .

umg=fs = ma
a=ug
a=0.4•10
a=4m/s2

Therefore max deacc is 4m/s2 and dist covered while this deacc is 25m
And final velocity is 0m/s as car will be stopped finally

V2=U2-2as
0 = U2 -(4)(25)2
U2=200m/s
U = 10root2 m/s