How long does it take the cars to meet?

[1irishman]

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.

 

[G01]

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...

 

[mykelgw]

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...

 

[1irishman]

The correct answer is 7.65 seconds. So it looks like you're right...