Question

The stopping distance (s) of a truck varies directly as the square of its speed (v). If a truck travelling at 50 mph requires 200 feet to stop, find the stopping distance for a truck travelling at 65 mph.

Answer 1

The distance is 338ft

Explanation:

Given

Represent distance with s and velocity with v:

When

`s = 200\ ft`

`v = 50mph`

Required

Determine the distance when velocity is 65mph

From the question, we understand that:

`s\ \alpha\ v^2`

Convert to equation

`s\ = kv^2`

Substitute 200 for s and 50 for v

`200 = k * 50^2`

`200 = k * 2500`

Make k the subject:

`k = (200)/(2500)`

`k = (2)/(25)`

To get s when v = 65.

Substitute 65 for v and 2/25 for k in
`s\ = kv^2`

`s = (2)/(25) * 65^2`

`s = (2)/(25) * 4225`

`s = (8450)/(25)`

`s = 338\\`

Hence, the distance is 338ft