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 identical conditions?

So the car would skid 4 times the initial skidding displacement under the identical conditions when the car's initial velocity is just double.

Explanation:

Under identical conditions when the brakes are applied for the same body moving with twice the initial speed then we can analyse using the equation of motion.

Initially:

...........................(1)

where:

final velocity of the car = 0 (because the car stops)

initial velocity of the car

acceleration of the car (here it is deceleration and hence taken with negative sign)

displacement of the car before stopping

Final condition:

Initial velocity is,

So,

.............................(2)

Now divide eq. (2) by (1)

So the car would skid 4 times the initial skidding displacement under the identical conditions when the car's initial velocity is just double.

hypothesising or postulating

we need to know the time interval during which the force acts. impulse of force = momentum change