Question

The German autobahns are the nationally coordinated motorway system in Germany and have no general speed limit, but the advisory speed limit is 81 mph.

Driving on the Autobahn in Germany, you have to brake suddenly. Let’s assume that the stopping distance of a car varies directly as the square of the velocity of car when the brakes are applied. A car moving at 85 mph can stop in 367 feet.
Write an equation that relates the stopping distance to the velocity.
What is the stopping distance of your car if you were moving at 95 mph?

Answer 1

The required equation is:
`s=0.0508v^2`

The stopping distance of your car if you were moving at 95 mph is 458.47 feet.

Explanation:

Consider the provided information.

Part (A)

Let us consider "s" is the distance "v" is the velocity and "k" is the constant of variation.

It is given that the stopping distance of a car varies directly as the square of the velocity of car when the brakes are applied

This can be written as:

`s=kv^2` ......(1)

It is given that A car moving at 85 mph can stop in 367 feet.

Substitute v=85 and s=367 in above formula and solve for k.

`367=k(85)^2`

`367=7225k`

`(367)/(7225)=k`

`0.0508=k`

Now to find the equation that relates the stopping distance to the velocity substitute the value of k in equation 1.

`s=0.0508v^2`

Hence, the required equation is:
`s=0.0508v^2`

Part (B)

Calculate the stopping distance of your car if you were moving at 95 mph.

Substitute the value of v=95 in
`s=0.0508v^2`

`s=0.0508(95)^2`

`s=0.0508* 9025`

`s=458.47`

Hence, the stopping distance of your car if you were moving at 95 mph is 458.47 feet.