How much time has elapsed when the cars are 200m apart?

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In summary, two cars, Car 1 and Car 2, are parked facing in opposite directions and accelerate at different rates. Car 1 accelerates at 5m/s^2 up to a maximum speed of 25m/s, while Car 2 accelerates at 4m/s^2 up to a maximum speed of 24m/s. When the cars are 200m apart, Car 1 takes 5 seconds to reach its maximum speed and Car 2 takes 6 seconds. Using the equation vf=vi+at, we can calculate that Car 1 has 137.5m remaining and Car 2 has 128m remaining when they both reach their maximum speeds. This means their separation is
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1irishman
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Homework Statement


Two cars are parked beside each other, facing in opposite directions. Car 1 accelerates at 5m/s^2 up to a max. speed of 25m/s, and Car 2 accelerates at 4m/s^2 up to a max. speed of 24m/s. How much time has elapsed when the cars are 200m apart?


Homework Equations


v=d/t
vf^2=vi^2+2ad


The Attempt at a Solution


Car 2
------
576=8d
d=72m
it takes car 2 3seconds to travel 72m

Car1
--------
625=10d
d=62.5m
it takes car 1 2.50seconds to travel 62.5m

So, the cars are 134.5m apart at this stage. They need to travel 200m-134.5m=65.5m before they are 200m apart.

So, if car 1 needs to travel 65.5m then this distance will take 65.5/25 = 2.62seconds
So, if car 2 needs to travel 65.5m then this distance will take 65.5/24 = 2.73seconds

This is as far as I could get. The answer is 6.83seconds. Please help me understand how they arrived at this solution?
Thank you.
 
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  • #2
How long does it take each car to reach its maximum speed? How far apart do they get while accelerating?
 
  • #3
"it takes car 2 3seconds to travel 72m"
"it takes car 1 2.50seconds to travel 62.5m"

These times are wrong
"v=d/t" is used when velocity is constant, which it is not when the cars start off.
Try using the equation, "vf=vi + at" to find how long it takes for each car to accelerate to its maximum speed. That should put you on the right track anyway.
 
  • #4
Using vf=vi+at
I figure out that Car 1 will take 5s to reach its max. speed, and Car 2 will take 6s to reach its max. speed.

I still don't know how to calculate the time elapsed when they are 200m apart. Please help?
 
  • #5
When car 1 reaches max speed, do the cars achieve 200 m separation? How about when car 2 reaches max speed? If not, how far do the cars still have to travel?

Hint: use the equation d=v0*t+(1/2)at^2
 
  • #6
when car 1 reaches max. speed it travels 187.5m right? When car 2 reaches max speed it appears it's gone beyond 200m up to 216m.
For car 1 i used: d=25(5)+1/2(5)(5)^2=187.5 so 200m-187.5=12.5m remaining? Is this right?
 
  • #7
No, because v0 is the car's initial speed. It's 0, not 25.
 
  • #8
Okay, so Car 1 has 137.5m remaining and Car 2 has 128m remaining?
 
  • #9
How can the two cars have different distances remaining? What did you get for the distance that the two cars have traveled once they both reach max. acceleration? Add them together and you get their separation.

A diagram might help.
 
  • #10
I think their separation is 134.5m.
 
  • #11
I'm lost, can someone please give me more hints?
 

FAQ: How much time has elapsed when the cars are 200m apart?

1. How can I calculate the time elapsed when the cars are 200m apart?

To calculate the time elapsed when the cars are 200m apart, you will need to know the initial distance between the cars, their velocities, and the acceleration of each car. You can use the equation d = ut + 1/2at^2 where d is the distance between the cars, u is the initial velocity, a is the acceleration, and t is the time elapsed.

2. What is the initial distance between the cars?

The initial distance between the cars can be any distance, as long as it is known. This could be the distance between the cars when they first start moving, or the distance between them at any point in their journey.

3. Do I need to know the velocities of both cars?

Yes, you will need to know the velocities of both cars to calculate the time elapsed when they are 200m apart. This is because the equation used to calculate time elapsed involves the initial velocities of the cars.

4. Can I use this equation for any type of motion?

Yes, this equation can be used for any type of motion as long as the initial distance, velocities, and acceleration are known. It is commonly used for calculating the time elapsed in situations involving constant acceleration, such as two cars moving at a constant speed.

5. Is there a simpler way to calculate the time elapsed when the cars are 200m apart?

If the cars are moving at a constant speed, you can use the equation t = d/v where d is the distance between the cars and v is the average velocity of the cars. This equation is simpler and can be used when the acceleration is constant.

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