How long does it take the cars to meet?

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Two cars start 300 meters apart and accelerate towards each other, with car 1 accelerating at 6.00 m/s² to a max speed of 30.0 m/s and car 2 at 5.00 m/s² to a max speed of 35.0 m/s. Calculations show car 1 reaches 75 meters in 5 seconds, while car 2 covers 123 meters in 7 seconds. The discussion involves finding the time when both cars meet, leading to an estimate of 7.69 seconds based on their combined distances. The correct answer is confirmed to be approximately 7.65 seconds, indicating that the initial calculations were close but slightly off. The thread emphasizes the importance of using equations of motion to determine the meeting point accurately.
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Homework Statement


Two cars are at rest, facing each other, and 300 metres apart.
If car 1 accelerates at 6.00m/s^2 up to a maximum speed of 30.0m/s and car 2 accelerates at 5.00m/s^2 up to a maximum speed of 35.0m/s, how long does it take the cars to meet?


Homework Equations


vf= vi + at
d= (vf + vi/2) * t



The Attempt at a Solution


Car 1
t = 5.00s
Car 2
t = 7.00s

After 5.0s Car 1 has traveled 75m
After 7.0s Car 2 has traveled 123m

That's as far as I got...i can't seem to figure out how long it takes for the two cars to meet..help please? I don't know if the numbers i have already are correct or not?
Thanks.
 
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HINT:

Find the equations of motions for both cars. You want the time at which both cars are at the same position x.

Thus, you have two equations and two variables...
 
Hi, well this is my first time on this site and i came across this question, I'm just about to take my prelim exams and found out i wasn't too sure about this question either...

This is what i did, if you have the answer say so :P...

1) Car A did 135 Metres after 7 seconds.
2) Therefore both cars have done 258 metres altogether after the 7 seconds.
3) (not sure about this...) Said both cars together are doing 65 metres per second from 7 seconds onwards.
4) Used the Equations to say that it takes the cars took .69 (to 2 d.p.) seconds to complete the last 42 metres.
5) Therefore it takes them 7.69 (to 2 d.p.) seconds to meet...

Not sure if I'm right...
 
The correct answer is 7.65 seconds. So it looks like you're right...
 

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