Answer:
156.7 m (nearest tenth)
Step-by-step explanation:
Define the variables:
If the distance needed to stop a car varies directly as the square of its speed:
[tex]\boxed{d \propto v^2 \implies d=kv^2}[/tex]
where k is the constant of proportionality.
Given:
To find the constant of proportionality, k, substitute the given values into the equation:
[tex]\begin{aligned}\implies 120&=k(70)^2\\k&=\dfrac{120}{70^2}\\k&=\dfrac{6}{245}\end{aligned}[/tex]
Substitute the found value of k back into the formula to create an equation for the given relationship:
[tex]\implies d=\dfrac{6v^2}{245}[/tex]
To find the distance (in meters) required to stop a car at 80 km/h, substitute v = 80 into the equation:
[tex]\implies d=\dfrac{6(80)^2}{245}[/tex]
[tex]\implies d=\dfrac{6\cdot 6400}{245}[/tex]
[tex]\implies d=\dfrac{7680}{49}[/tex]
[tex]\implies d=156.73469...\; \sf m[/tex]
[tex]\implies d=156.7\; \sf m\; (nearest \;tenth)[/tex]
Therefore, the distance required to stop a car at 80 km/h is:
