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A typical automobile under hard braking loses speed at a rate of about [tex]7.2 \, \text{m/s}^2[/tex]. The typical reaction time to engage the brakes is [tex]0.55 \, \text{s}[/tex]. A local school board sets the speed limit in a school zone such that all cars should be able to stop in [tex]3.6 \, \text{m}[/tex]. What maximum speed does this imply for a car in the school zone?

Answer :

Answer:

4.3 m/s

Explanation:

a = rate at which the automobile loses speed = - 7.2 m/s²

v₀ = initial maximum speed of automobile

t' = reaction time for applying the brakes = 0.55 s

d = distance available for stopping the vehicle = 3.6 m

d' = distance traveled while applying the brakes = v₀ t' = (0.55) v₀

v = final speed after the vehicle comes to stop = 0 m/s

Using the equation

v² = v₀² + 2 a (d - d' )

0² = v₀² + 2 (- 7.2) (3.6 - (0.55) v₀)

v₀ = 4.3 m/s

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