Question

The distance needed for a car to stop depends on how fast the car is travelling. This distance can be calculated by adding the thinking distance and the braking distance. For example: at 30 miles per hour Here are the formulae to work out the thinking distance and the braking distance for a car travelling at miles per hour. Thinking distance = feet Braking distance = feet A car is travelling so that its braking distance is 125 feet. How fast is the car travelling? miles per hour

Answer 1

Missing Parts

Here are the formulae to work out the thinking distance and the braking distance for a car traveling at V miles per hour.

Thinking distance = V feet

`\text{Braking distance = }(V^2)/(20)$ feet`

(a) A car is traveling at 70 miles per hour. What is the total stopping distance for this car? feet

(b) A different car is traveling so that its braking distance is 125 feet. How fast is the car traveling? miles per hour

Answer:

(a)2520 feet

(b)50mph

Explanation:

Total Stopping Distance = Thinking Distance + Braking Distance

Given that for a car traveling at V miles per hour:

Thinking distance = V feet

`\text{Braking distance = }(V^2)/(20)$ feet`

We have:

`\text{Total Stopping Distance=} (V+(V^2)/(20))$ feet`

(a)V=70 miles per hour

`\text{Total Stopping Distance=} 70+(70^2)/(20)$=2520 feet`

The total stopping distance for a car traveling at 70 miles per hour is 2520 feet.

(b)

Braking Distance = 125 feet

`\text{Braking distance = }(V^2)/(20)$ feet`

Therefore:

`(V^2)/(20)=125\\\\V^2=125* 20\\V^2=2500\\V^2=50^2\\V=50$ miles per hour`

A car with a braking distance of 125 feet is traveling at a speed of 50mph.