When an automobile moving with a speed of 36 km per hour creatures are incline root of 30 degree angle if its coefficient of friction is 0. 1 and the engine is switched off then how much distance will it cover to come at rest 1 g is equal to 10 m per second square?
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P = f + W Sinθ
But, f = μW cos θ = μmg cosθ
Where m = mass of automobile
P = μmgcosθ + mg sinθ
a = p/m = μmgcosθ + mgsinθ/m
= μgcosθ + gsinθ
=(0.1 x 10 x √3/2) + (10 x 1/2)
= 5.866 m/s²
If we consider the law of motion
Distance traveled after when the engine will be switched off
v² = u² - 2as
=> s = u²-v²/2a
= (36x5/18)² - 0/2 x 5.866
= 8.52m
the final velocity v after coming to rest is zero.
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