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

[1irishman]

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.

 

[Doc Al]

How long does it take each car to reach its maximum speed? How far apart do they get while accelerating?

 

[Wiseman101]

"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.

 

[1irishman]

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?

 

[ideasrule]

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

 

[1irishman]

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?

 

[ideasrule]

No, because v0 is the car's initial speed. It's 0, not 25.

 

[1irishman]

Okay, so Car 1 has 137.5m remaining and Car 2 has 128m remaining?

 

[ideasrule]

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.

 

[1irishman]

I think their separation is 134.5m.

 

[1irishman]

I'm lost, can someone please give me more hints?