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

Answer:

The distance is 338ft

Step-by-step 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:

$k = \frac{200}{2500}$

$k = \frac{2}{25}$

To get s when v = 65.

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

$s = \frac{2}{25} * 65^2$

$s = \frac{2}{25} * 4225$

$s = \frac{8450}{25}$

$s = 338$

Hence, the distance is 338ft