Question

4. The distance needed to stop a car varies directly as the square of its speed. It

requires 120 m to stop a car at 70 km/h. What distance is required to stop a car
at 80 km/h?

Answer 1

156.7 m (nearest tenth)

Explanation:

Define the variables:

• Let d = distance in meters.
• Let v = speed in kilometers per hour.

If the distance needed to stop a car varies directly as the square of its speed:

`\boxed{d \propto v^2 \implies d=kv^2}`

where k is the constant of proportionality.

Given:

• d = 120 m
• v = 70 km/h

To find the constant of proportionality, k, substitute the given values into the equation:

`\begin{aligned}\implies 120&=k(70)^2\\k&=(120)/(70^2)\\k&=(6)/(245)\end{aligned}`

Substitute the found value of k back into the formula to create an equation for the given relationship:

`\implies d=(6v^2)/(245)`

To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:

`\implies d=(6(80)^2)/(245)`

`\implies d=(6\cdot 6400)/(245)`

`\implies d=(7680)/(49)`

`\implies d=156.73469...\; \sf m`

`\implies d=156.7\; \sf m\; (nearest \;tenth)`

Therefore, the distance required to stop a car at 80 km/h is:

• 156.7 m (2 d.p.).