Question

A 1000-kg car is moving at 40.0 km/hr when the driver slams on the brakes and skids to a stop (with locked brakes) over a distance of 20.0 meters. How far will the car skid with locked brakes if it is traveling at 120. km/hr?

Answer 1

Answer:

 skid distance = 180 m  

Explanation:

given,

mass of the car = 1000 Kg

speed of the car = 40 Km/hr

distance to stop = 20 m

if speed is now = 120 Km/he

distance to stop = ?

from given question we can state that,

Work done by the friction is equal to the change in kinetic energy of the car.

       $W= \dfrac{1}{2}mv^2$............(1)

And we also know that work is directly proportional to displacement

               W = F × x...........................(2)

from the equation (1) and (2)

        x ∝ v²

now,

   here velocity is increased from 40 km/h to 120 km/h means velocity is increase 3 times

so displacement will be equal to 3² or 9 times

hence, skid distance will be equal to 9 x 20 = 180 m

 skid distance = 180 m