How long does it take the cars to meet?

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Homework Help Overview

The problem involves two cars starting from rest and accelerating towards each other from a distance of 300 meters. Car 1 accelerates at 6.00 m/s² with a maximum speed of 30.0 m/s, while Car 2 accelerates at 5.00 m/s² with a maximum speed of 35.0 m/s. The objective is to determine the time it takes for the cars to meet.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the equations of motion for both cars and the need to find the time when both cars are at the same position. Some participants share their calculations and results, questioning the correctness of their approaches.

Discussion Status

There are various attempts to solve the problem, with some participants providing calculations and others offering hints. While one participant suggests a method involving equations of motion, another expresses uncertainty about their results. A participant claims a specific answer, but there is no consensus on the correctness of the calculations presented.

Contextual Notes

Participants are preparing for exams, which may influence their approach and urgency in seeking clarification. There is uncertainty regarding the correctness of the initial calculations and the assumptions made about the cars' movements.

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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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