Question

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?

Answer 1

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.

Step-by-step 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

`S=(Vf^(2)-Vi^(2))/(2a)`

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

Answer 2

It could be seen above that the speed of the vehicle is as twice as fast. As a rule, if the speed is doubled, the distance would likely increase. So if the speed is 2^2, it will increase the distance, having the product of 4. So the answer to the given problem above is that the distance of the car that have skidded would produce four times further.