Question

You are driving along a country road when you suddenly notice a log in the road ahead of you and immediately apply your brakes. You travel a distance of s(t) = 66 t - 6 t^2 feet in t seconds after you hit the brakes.

The log was 180 feet ahead of you when you noticed it, which unfortunately wasn't soon enough.

At what time (in seconds) did you hit the log?
How fast were you going (in ft/sec) when you hit it?

Answer 1

which grade is it?

Answer 2

well since 180 is the distance you know distance is a function of time. so if you set the function = to 180 then you can solve for t

Answer 3

then your speed will be distance/time.

Answer 4

oh i see i need a s = d/t equation

Answer 5

dude theres something wrong with the equation
it is coming 2094ft/sec

Answer 6

what did you get for your time.

Answer 7

well u differentiate the equation and then put 180 in place of t and u get ur speed

Answer 8

i see

Answer 9

180 is not a time.

Answer 10

so i got s(t) = 66-6t^2
v(t) = -12t
a(t) = -12

Answer 11

what else will u substitute for t dude

Answer 12

s(t)=180 because that is distance as a function of time.

Answer 13

yeah jgeurts u got it right

Answer 14

if s(t) = 180 then i get
t^2 = -19???

Answer 15

dont do it that way
what u got is right jgeurts

Answer 16

looks like you dropped a t when you took the derivative of your first function it should have been 66-12t

Answer 17

as long as the first function wasnt a typo. because i see 66t-6t^2=s(t)

Answer 18

what are u saying man
s(t)=180 has t^2 and not 12 t

Answer 19

so how fast was i going?

Answer 20

i was just correcting the first derivative of the original function.

Answer 21

-12t

Answer 22

but i can't solve for t

Answer 23

u don't have to
u can write the speed in terms of a variable

Answer 24

i need to

Answer 25

was your original function s(t)=66t-6t^2?

Answer 26

yes….

Answer 27

then your first derivative is wrong. it should have a constant in it.

Answer 28

so i got s(t) = 66t-6t^2
v(t) = 66-12t
a(t) = -12

Answer 29

typo

Answer 30

yeah and t=5 or 6
i mean it has 2 values

Answer 31

yep. but you still have to find your time. so the only way i can see to do that is to use your distance on your original function to get time.

Answer 32

dude
i just gave u the value of time

Answer 33

how do i do distance on my original function?

Answer 34

thanks Rahul, but how did u get it?

Answer 35

your distance is 180 feet from the log. and dude.. i posted that at the same time as you. get your panties out of a bunch...

Answer 36

180=66t-6t^2 like i said a while back.

Answer 37

u solve the eqn 66t-6t^2=180
get t
then put it in -12t to get the speed

Answer 38

are we done

Answer 39

-12t is not the first derivative of the position function here.

Answer 40

66-12t is

Answer 41

sorry i mean 66-12t

Answer 42

my mistake

Answer 43

hey don't i get a medal?

Answer 44

66t -6t^2 = 180
t = sqrt19

Answer 45

plug sqrt19 into v(t)?

Answer 46

dude jgeurts
do u even know maths

Answer 47

the problem isnt finished. uh. thats not what i was thinking it should be 5 or 6.
hey man. there is no reason to be rude.

Answer 48

lol im so bad, I'm going off that original screwed up equation

Answer 49

your 2 possible answers for time are 5 and 6 since its a quadratic equation you will have 2 possible answers.

Answer 50

it is 5 or 6
help urself

Answer 51

you will take your time and plug it into your velocity function to get your velocity.

Answer 52

ok, its 5 then plug it into 66 -12t so that would be 6s?

Answer 53

100% thank you both!

Answer 54

6s? what do you mean by that. you will have 6 as your answer. do you mean 6 feet per second?

Answer 55

yeah fps

Answer 56

sweet. then that is correct for time 5