Question

The braking distance (d) needed to stop a car varies directly with the square of the car's speed (s). A car going 30 mph needs 40 feet of braking distance to come to a complete stop. How many feet of braking distance would the same car, under the same conditions need going 70 mph? (Round the answer to the nearest whole number.)
Question 9 options:

a) 218 feet

b) 92 feet

c) 53 feet

d) none of these

Answer 1

The equation that models the braking distance is
\[d=ks ^{2}\ ...........(1)\]
where k is a constant of proportionality. The value of k can be found by rearranging equation (1) and plugging in the given values:
\[k=\frac{d}{s ^{2}}=\frac{40}{30^{2}}\]
To find the braking distance when the car is doing 70 mph just plug the values for k and s into equation (1). Can you do that?

Answer 2

@SavannahWillett Are you there?

Answer 3

Yes

Answer 4

The required braking distance is
\[d=\frac{40}{30^{2}}\times 70^{2}=\ ?\]

Answer 5

so just 70??

Answer 6

Oh, I didn't see the times symbol

Answer 7

93.3!

Answer 8

kropot posted the equation

you have to do what the equation says: 40 divided by 30^2. then multiply by 70^2

Answer 9

you have to square the speeds...

Answer 10

Oh. Then it would be 213/
I have a really crappy lap top and the screen is going out. I can't see.

Answer 11

omj. 217.78*****

Answer 12

yes. round to the nearest foot... 218

Answer 13

Ohkay.
What is the equation exactly? And why is it that? If that makes sense

Answer 14

it says
distance (d) needed to stop a car varies directly with the square of the car's speed (s).

shorten that up to

distance varies directly with speed squared

"varies directly" is math code for
distance = some number times speed squared
we call the "some number" k. and call distance d , and call speed s
d = k s^2

does that make sense ?

Answer 15

So it's the opposite of varying indirectly?

Answer 16

once you get that equation, you fill in a known d distance and associated speed to find k

they say 30 mph needs 40 feet o
replace d with 40 and s with 30 to get


d = k s^2
40 = k 30^2
k = 40/30^2

put k into the equation, to get

d = 40* s^2/30^2

now you can solve for any speed.

Answer 17

Ohhhh, thank you!!!

Answer 18

**So it's the opposite of varying indirectly?**

the easiest problem is

y varies directly with x
which matches the equation y = k x
they give you an x and y. you figure out k. they give you a different x, you can find the corresponding y

Answer 19

the next easiest is

y varies indirectly with x
that means

y = k/x

indirectly means you divide by x instead of multiply. memorize this, or do so many problems it sinks in.

Answer 20

more tricky is

y varies directly with the square of x

which means
y = k x^2 (x is squared)

this is the problem you just did

Answer 21

you sometimes see
y varies indirectly with the square of x

y = k/x^2

the reason this one is interesting is that is the relation with gravity... Newton (somehow) figured it out.

Answer 22

How do you know if it is the square of x??

Answer 23

for this problem ?

Answer 24

can you be more specific ?

Answer 25

Any tine

Answer 26

Like with word problems. How do you know the difference between y varies with x and y vaires with the square of x?

Answer 27

the problem will tell you (except in the real world where you have to guess and see if it makes sense)

but in algebra, they will tell you. In this problem they say

"The braking distance (d) needed to stop a car varies directly with the square of the car's speed (s)."

the phrase " square of the car's speed (s)." means "square of s" or "s squared"
or \( s^2 \)

Answer 28

Oh! I guess I must have just read right over that. Thank you for clearing up my confusion!!!