You slam on the brakes of your car in a panic, and skid a certain distance on a straight, level road. if you had been traveling twice as fast, what distance would the car have skidded, under the same conditions?

If the speed would be doubled, the distance traveled by the vehicle will be FOUR times. It can be proved by 3rd equation of motion.

Explanation:

When the brakes are applied, frictional force acts on the tires which decreases the speed. Eventually the car will stop. This frictional force is nearly independent of the speed hence by applying 3rd equation of motion, we can find the distance traveled.

2aS = Vf²-Vi²

For Vf=0

S=-Vi²/2a

Vi-new = 2*Vi

S-new = -(Vi-new)²/2a

S-new = -(2*Vi)²/2a

S-new = -4Vi²/2a

S-new = 4.S

Here

Vf= Final Velocity i.e. 0m/s²

Vi= Initial Velocity

a= Deceleration (Negative Acceleration)

S= Distance covered by vehicle