Physics word problem- velocity, acceleration, time

[meredith]

Homework Statement

two cars are traveling along a straight road, one behind the other. the first is traveling at a constant velocity of 12 m/s. the second, approaching from the rear, is traveling at 25 m/s. when the second car is 200m behind the first, the driver applies the brakes, producing a constant acceleration of -0.20 m/s^2. will the cars crash and if so, where and when?

Homework Equations

acceleration = (change in velocity)/(change in time)
change in dispacement = (Initial velocity) (time) + (1/2) (acceleration) (time sqaured)
velocity = (acceleration) (time)

The Attempt at a Solution

i got they woud crash after 50 meters? but i don't think that's right :(

 

[tiny-tim]

Welcome to PF!

Hi meredith ! Welcome to PF!

Show us what you did, and then we can see where it went wrong.

 

[MrEnergy]

If the second car had a velocity of 12m/s^2, then they wouldn't crash, so we try to see if they do;

25 - 0,2t = 12 => t=65s

in 65 seconds we see that the cars actually crash. So its time to see where they actually crash..

so in "t" seconds after the break, the second cars velocity will be "25-0,2t" and first velocity was "25". Time past is "t" and the length passed is; "12t+200m". So if we equalize these, we have;


(25+25-0,2t)*t/2=12t+200

then we find t=13(approximately) (At the 13th second they crash) so then we have a velocity of "22,4m/s^2" of the second car when they crash and this hapens after "346" meters passed...

I hope I am correct!

 

[tiny-tim]

(25+25-0,2t)*t/2=12t+200

Yes … but how did you get "t=13(approximately)" ?

This is a quadratic equation … find the exact solution!

 

[Sakha]

I think you're wrong.
First I think we need to set an equality of the distance, having 25t-.2t²+200=12t.
So we solve for t, getting t₁=-12.85s, and t₂=77.85s, so t₂ is out real answer.
Then you plug t in a distance formula. So based on the first car you have d = 12m/s(77.85s)=934.2m.

 

[MrEnergy]

Sakha, after 65 seconds second car's velocity becomes 12m/s^2, and they are not supposed to crash with same velocities. So that your t2=77 second is impossible...

The right answer is 13 seconds(I could'nt solve but you can use a program to get the exact number). After 13 secs they crash...

 

[tiny-tim]

… I could'nt solve …

Yes you can!

It's 0.1 t² - 13t + 200 = 0, so the answer is … ?

 

[MrEnergy]

I mean't i didn't work for it:P Just used a program.

 

[rmax58]

i just registered for this site today and i was wondering how i go about asking questions?

 

[tiny-tim]

Welcome to PF!

i just registered for this site today and i was wondering how i go about asking questions?

Hi rmax58! Welcome to PF!

Go to the https://www.physicsforums.com/forumdisplay.php?f=152" forum, choose the appropriate sub-forum, and click the "NEW TOPIC" button.

(and read the homework FAQs! )