Physics help????? Kinetic Energy=1/2mv^2???????

Question

A car traveling at 50 km/hr skids a distance of 35 m after its brakes lock. Estimate how far it will skid if its brakes lock when its initial speed is 100 km/hr.

Answer 1

I took different approach, but got the same answer :)

1. you know that car was traveling 50 km/h and skid distance 35 meters. From this information you can figure out the acceleration. The equation is v^2 = vo^2 + 2ad
v- final speed (which we know is 0 because car stops)
vo - initial speed which is 50 km/h = 50km/h x 1000m/km x h/3600 s = 13.9 m/s
d - our distance which is 35 m
a - our unknown

v^2 = vo^2 + 2 a d (v=0)
a = - vo^2 / 2d (the minus symbolizes slowing down)
a = - 13.9^2 / 2 x 35
a = - 2.76 m/s

Now when you know acceleration you can use the same equation to solve for the distance with 100 km/h speed
v - final speed is again 0
vo - is 100 km/h = 100km/h x 1000m/km x h/3600s = 27.8 m/s
a is -2.76 m/s
d is unknown

v^2 = vo^2 + 2ad (v=0)
d = -vo^2/2a
d = - (27.8)^2 / [2 (-2.76)]
d = 140 m

Hope this helps.

Answer 2

The braking force is constant, so the work done is proportional to distance. This means that braking distance is directly proportional to initial kinetic energy. But initial kinetic energy is proportional to the square of initial velocity, so braking distance is also proportional to the square of initial velocity. So, double the velocity and you quadruple the braking distance.