Mechanics question

[lektor]

This question is just a practice for creating equations for suiting situations but i feel as if I've taken the completely wrong appoach..


Two cars begin to move toward each other simultaneously along a straight road. Car 1 starts from point A at a speed of V1; Car 2 starts at point B at a speed V2.The acceleration of car 1 is a1; it is directed toward A,
The acceleration of car 2 is a2; it is directed toward B. In the process of motion, the cars meet twice; the time interval between the meetings is t. Find the distance between A and B.

Some help would be great, so far my approach was using kinematic formulas.

I finished with D = \sqrt{\frac{Vi1*T*a1*T^2}{Vi2*T*a2*T} }

Sorry about the mathlatex in currently reading the guide.

[ramollari]

The units in your result don't agree. They are ms, and not m.

I came up with this formula:


D = \frac{(v_{01} + v_{02})^2 - (\frac{a_1 + a_2}{2\Delta t})^2}{2(a_1 + a_2)}

[lektor]

The units in your result don't agree. They are ms, and not m.

I came up with this formula:


D = \frac{(v_{01} + v_{02})^2 - (\frac{a_1 + a_2}{2\Delta t})^2}{2(a_1 + a_2)}

Your Answer looks quite well thought out, could you please give some explanations of how you reached it :)?

[ramollari]

Express the positions x of both vehicles in terms of time. Equalize them, and you get a quadratic equation for time, that of course gives two results. Then, the procedure is simple:

\Delta t = \frac{\sqrt{\Delta}}{a}

Both Delta and a will contain the quantities D, a1, a2, v01, v02. So, solve for D to arrive at that result.