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Two objects facing each other over a distance of 88m start moving from rest at an acceleration of 0.3m/s^2 and 0.2m/s^2 respectively, after how long do they intersect?

I've tried everything to find the answer and using brute force I found that they will intersect after 18.8 seconds because object a will have moved 53.016m and object b 35.344m but I don't know how to plot the problem so I don't have to use brute force.

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  • $\begingroup$ Can you explain your brute Force method? $\endgroup$ – Protein Sep 19 '20 at 15:14
  • $\begingroup$ Show your work so far. As a hint -- do you know the equation for position vs. time given steady acceleration? $\endgroup$ – TimWescott Sep 19 '20 at 15:43
  • $\begingroup$ Your 'brute force' results are certainly correct. You should show how you did that. $\endgroup$ – Gert Sep 19 '20 at 15:48
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    $\begingroup$ I calculated displacement given different times for each object and kept doing that until both displacements added up to 88m and that lead me to 18.8 seconds. $\endgroup$ – Viktor Sep 19 '20 at 15:56
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Could you solve the problem if one object was stationary and the second object was accelerating towards the first at $0.5$ m/s^2 ? Can you see how this might help you solve the original problem ?

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The simplest method is to solve this problem from the frame of one of one of the particles.

Alternatively you can use the displacement equations of particles.

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HINT: You need to collapse the 2 equation for the distance that is :
$x = \frac{1}{2}at^{2}+x_{0}$
knowing that
$x_{firstVehicule} = x_{secondVehicule}$
when they intersect.

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