Question

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

Answer 1

Answer:

156.7 m (nearest tenth)

Step-by-step 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:

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

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

$\implies d=\dfrac{6v^2}{245}$

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

$\implies d=\dfrac{6(80)^2}{245}$

$\implies d=\dfrac{6\cdot 6400}{245}$

$\implies d=\dfrac{7680}{49}$

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

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

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

• 156.7 m (2 d.p.).