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?

A) It would have skidded half as far.
B) It woud have skidded twice as far.
C) It would have skidded 4 times farther.
D) It would have skidded √2 times farther.
E) It is impossible to tell from the information given.

Answer 1

C) It would have skidded 4 times farther.

Step-by-step explanation:

velocity at some time t is given as:

v(t)=v0−a0t

(See Picture attached)

where v0 is the initial velocity. time t=v0/a0 as car stops.

The position is the integral of the velocity.

x0 is the car position after applying brakes.

So if initial velocity is doubled the distance traveled becomes 4 times the initial distance.

Answer 2

C) It would have skidded 4 times farther

Step-by-step explanation:

The distance the car skidded is given by:

`X1 =(V^2)/(2*a)`

The acceleration is the same on both scenarios since it depends on the surfaces.

If the speed is now 2*V:

`X2 =((2*V)^2)/(2*a)`

`X2 =(4*V^2)/(2*a)`

`X2 =4*X1`

We can conclude that It would have skidded 4 times farther