Q: Explain how the range of your car’s headlights limits the safe driving speed at night .

Sol:When a car moves , there is a rolling friction between the tyres and road . Rolling friction is smaller in comparison to sliding friction . When the brakes are applied , the wheels are clamped and hence arises enormous sliding friction . This sliding friction stops the car If S is the range of headlight , then the car must be stopped within this distance . Suppose M be the mass of the car and μ_{s} be the coefficient of sliding friction .

Then limiting frictional force = μ_{s} M g = M a ; Where ‘ a ‘ is the retardation produced .

a = μ_{s} g

But , $ \displaystyle v_{safe \, speed}^2 = 2 a S $

$ \displaystyle = 2 \mu_s g S $

$ \displaystyle v_{safe \, speed} = \sqrt{2 \mu_s g S} $