Question

The stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car travelling 70 mph can stop in 270 ft, how many feet will it take the same car to stop whenit is travelling 60 mph?

Answer 1

d = k r [stopping_distance = (constant of variation)(speed)]
270 = k (70)
k = 27/7

Now that we have found k, substitute k and the new speed into the initial equation.
d = (27/7)(60) = 231 and 3/7 feet

Answer 2

hmmm, I am already confused.

Answer 3

When you have direct variation equations, then the form is:
FIRST_NUMBER = VARIATION_CONSTANT * SECOND_NUMBER

The problem will give you two numbers that for one scenario. Then it will ask you about a second scenario where it gives you one number, and you must find the second.

So, to solve these problems, you must find the constant of variation as I have shown above.

Answer 4

Ok, I am totally confused.

Answer 5

OR
You can treat the problem like a proportion and use cross multiplication (which ever one makes more sense to you)
\[270/70 = x/60\]

Answer 6

The stopping distance compares to the speed - this is a ratio. (270/70)

A proportion is when we compare two ratios. I have an unknown distance (x) and a speed of 60. (x/60)

This will give you (270)(60)/(70) = 231 and 3/7 feet

Answer 7

Let's try this one....stopping distance d of a car after the brakes are applied varies directly as the square of the speed r. If a car traveling 70 mph can stop in 270 ft, how many feet will it take the same care to stop when it is traveling 80 mph?

Answer 8

Then
270/70 = x/80
Cross Multiply
270(80)=70x
Divide by 70
x=270(80)/70

308 and 4/7 feet

Answer 9

That is not correct.

Answer 10

First the relationship is such that the stopping distance varies directly with square of speed ie.
D(stopping distance) = K (proportionality constant) * r^2 (speed)
The units in the given relationships are different to each other….since the question is asking us to calculate how many feet…..lets first convert the miles per hour into ft per sec
70 miles/hr=1026.36 ft/s (verify yourself)
80 miles/ hr=1172.98ft/s
Now lets use the given condition(stops at 270 ft when 70mph) to find the constant ‘K’
D=K*r^2
270 =K*(1026.36)^2
K=.000256
Plug the value of K to find the stopping distance when the speed is 80 miles/hr ie. 1172.98ft/s
D=.000256*( 1172.98)^2
D=352.22 ft

Answer 11

for 60mph ie. 879.73ft/s
D=.000256*(879.73)^2
D=198.12ft

Answer 12

My apologies for not noticing the word 'squared'.

Answer 13

There is no need to convert to ft/s for this problem. The natural answer will be in feet.

270/70^2 = x/80^2

Cross Multiply
270(6400)=4900x

Divide by 4900
x=270(6400)/4900 or 270(64)/(49)

352 and 32/49 feet