Question

2.The distance needed to stop a car after applying the brakes varies directly with the square of the car's speed. Thetable below shows stopping distances for various speeds.60Speed (mph) 10 20 30 40 5070Distance (ft) 6.25 25 56.25 100 156.25 225 306.25Determine the average rate of change in braking distance, in ft/mph, between one car traveling at 50 mph and onetraveling at 70 mph. Explain what this rate of change means as it relates to braking distance.

Answer 1

Given

Table

Procedure

Point A

50 mph 156.25 ft

Point B

70 mph 306.25 ft

Rate of change

`\begin{gathered} (306.25-156.25)/(70-50) \\ 7.5\text{ ft/mph} \end{gathered}`

A rate of change is a rate that describes how one quantity changes in relation to another quantity.

In this case, it means that increasing the speed by 1 mph will increase the braking distance by 7.5 ft.