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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

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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.