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# A vehicle moving with velocity, Vo on a rough horizontal road is brought to rest in a distance, s. If the coefficient of static friction between the tyres is µ, show that it is independent of the mass of the vehicle. Hence calculate s, when µ = 0.5 and V0 = 90 kmh-1.  [g =10 ms-2]

Ram Kushwah
108 Points
one month ago
Here u = V,v=0  Distantance=s
So  v²= u²+2as

0= V0²  + 2as
a  =  – V0²  / 2s
Thus force  between tyres and road
F = ma = – mV0²  /  2s …..................(1)
Now  force due to friction
F= – μmg..........................................(2)
From(1) and (2)

– mV0²  /  2s = – μmg.
2sμg. = V0²
s = V0² / μg
Hence distance s is independent of  mass m
Putting all the given values we get
s=(90*1000/3600)²/0.5*10   ( as 1 km/h=1000/3600 m/s)
=625/5
=125 m