How long does it take the cars to meet?

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In summary, the two cars are initially 300 metres apart and are accelerating at different rates up to maximum speeds. To determine how long it takes for the cars to meet, we can use the equations of motion. After 5 seconds, Car 1 has traveled 75 metres and after 7 seconds, Car 2 has traveled 123 metres. By adding these distances together, we get a total of 258 metres after 7 seconds. Since the cars are traveling at a combined speed of 65 metres per second after this time, it takes them 0.69 seconds to cover the remaining 42 metres and meet. Therefore, the total time it takes for the cars to meet is 7.69 seconds.
  • #1
1irishman
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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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  • #2
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...
 
  • #3
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...
 
  • #4
The correct answer is 7.65 seconds. So it looks like you're right...
 

1. How do you calculate the time it takes for cars to meet?

The time it takes for cars to meet can be calculated by dividing the distance between the two cars by the sum of their speeds. This formula is known as the "time equals distance over speed" formula.

2. What information do you need to calculate the time it takes for cars to meet?

To calculate the time it takes for cars to meet, you will need to know the distance between the two cars and their respective speeds.

3. Can you calculate the time it takes for cars to meet if they have different speeds?

Yes, the time it takes for cars to meet can still be calculated even if they have different speeds. As mentioned before, you will need to know the distance between the two cars and their respective speeds to calculate the time.

4. How does the distance between the two cars affect the time it takes for them to meet?

The shorter the distance between the two cars, the faster they will meet. This is because the distance affects the numerator in the time calculation formula.

5. Is there a way to speed up the time it takes for cars to meet?

The only way to speed up the time it takes for cars to meet is by increasing the speed of one or both cars. This will decrease the denominator in the time calculation formula, resulting in a shorter time.

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