Not sure which formula to use for this problem

[ash312]

Homework Statement

A women is traveling at 50km/h, she sees a stop sign and takes 1.4 s to react, she starts decelrating at 2.3m/s and there is a broken bridge 150 m ahead of the sign.
Is she going to stop in time?

Homework Equations

I am not sure but i think one of these equations can be used:

DeltaD = v1 * delta T + 1/2 + a (delta t)^2

V2 = v1^2 +2 * a * delta d

delta D = (v1+v2) / 2 * Delta TDelta D = V2 * Delta T - 1/2 * a (delta T)^2

The Attempt at a Solution

 

[renaldocoetz]

the reason they tell u that there's a broken bridge 150m ahead, is that they want u to use ure equations of kinematics to work out what her displacement wil be if she decellerates from 50 km/h to 0 , at 2,3m/s. remember to change it into m/s before u start.

 

[renaldocoetz]

also what do u think is the importance of the 1,4s reaction time?

 

[ash312]

I remember changing it to m/s and i got 13.8 m/s converting it from 50 km/h. I think i should use the Delta D = (v1-v2)/2 * Delta T. And i don't no the improtance of the 1.4 s reaction time

 

[renaldocoetz]

they tell you that she has 150m to stop in. But she took 1,4secs to react. in other words she still drove at the initial speed for 1,4 secs before she startd to decelerate. Work out how far she drove in that time and deduct that from the 150m to know what distance she has to stop.

 

[ash312]

Ok, so she traveled 31.74 m after deducting it from 150 i got 118.26. So she has to stop within 118.26 m. Now what formula do i use to figure out if she stopped in time?

 

[renaldocoetz]

how did u get 31,74?

D = V.t

 

[ash312]

OH right right! i accidently times it by 2.3! ok so its 19.32 m then she started to decelerate, then after subtracting it by 150 it is 130.68. So she has 130.68 m to stop

 

[renaldocoetz]

use equation: V² = V₀² + 2aD

with D being displacement
remember the value of a is negative during decelerationBTW this is during 2nd part,...when she starts decelerating.

 

[ash312]

OK i did it but i don't think its right:

= 13.8^2 + 2 (-2.3) (130.68)
= 190.44 + (-0.3) (130.68)
= 190.44 + (-39.204)
= 151.236

Do i square root the answer? if this is right...

 

[renaldocoetz]

D in the equation is the distance it takes her to go from 13,8 m/s to 0 m/s. in other words to stop. which is the answer u need.
Do u understand why u can not substitute 130,68 into it?

 

[ash312]

ok.. i understand, 130.68 can go into it because that is the distance she has to stop not the distance it takes her to stop.. so what do i put in instead of 130.68? 19.32?

 

[renaldocoetz]

no u don't put anything into it. U want to find the value of D. U can't find the value of a variable if u substitute another value into it.

put all values into equation, leaving D as it is. Then calculate the value of D

 

[ash312]

ok, so the value of d is 190.14?

 

[renaldocoetz]

nope


V² = V₀² + 2aD


What are the values of each variable? and which one do u want to calculate?

 

[ash312]

V^2 = 190.44 + 2 * (-2.3) D

i need to calculate D

 

[renaldocoetz]

good . what's the value of V^2 ?

 

[ash312]

185.84? sorry it took so long... i didnt no the reply was in the second page.. i was waiting for it in the first page! :=)

 

[renaldocoetz]

no worries

V² is the final speed, right? so what should the car's final speed be if he stopped? surely not 185

 

[ash312]

If she stopped then it would be 0.

 

[renaldocoetz]

K so do u agree that this is what we have now:

V² = V₀² + 2aD

0 = (13,8)² + 2(-2,3)D



now calculate D

 

[ash312]

Ok, do i square root my answer? If i do then i got 13.6

 

[renaldocoetz]

V² = V₀²+ 2aD

-(13,8)² = + 2(-2,3)D



no need to square root just calculate

 

[ash312]

in that case i got 185.84

 

[renaldocoetz]

ure making a mistake somewhere

-(13,8)^2 = + 2(-2,3)D

- 190,44 = -4,6D ...now divide by (-4,6) to find D

 

[ash312]

-19.6?

 

[renaldocoetz]

190,44 devided by 4,6 = 19,6? must be something wrong with ure calculator mate :)
The minusses both fall away

 

[ash312]

ok.. so, wats the answer? 19.6?

 

[renaldocoetz]

no
190,44/ 4,6 = 41,4 m

 

[ash312]

OMG! i made a careless mistake... i forogot to put in the 1 before 190.44...! :( ok then she stopped within 41.4 m. Which means she didnt fall over the bridge rihgt?

 

[renaldocoetz]

thats correct yeah. lucky girl

 

[ash312]

LOL! yes She gets to survive! we saved her! Anyway Thanks alot! i think i learned somthint here!