Hello everyone, I have yet another problem that I just can't seem to work my way around. Here it is:(adsbygoogle = window.adsbygoogle || []).push({});

A particle starts from rest and at the origin. The particle is cofined to motion along a straight line. The particle accelerates uniformly with magnitude a for a time interval t, then travels at a constant velocity for the same time interval t, followed by a constant decceleration of magnitude -a for a time interval T, different from that of t. That's the question. Here's the problem;

In terms of the given time interval t, at what time does the particle return to the origin?

Okay, I understand that there are multiple ways of looking at this problem. I approached as a graphical solution with the motion formulas (kinematics if you will). I made a velocity vs time graph, superimposed on the accel vs time graph and represented that the positive trapezoid had an equal area as the triangle below the time axis. the issue lay in the algebra of the kinematics and the adding of the displacements. My final answer was in a strange quadratic form, but I have a feeling that the answer is like 7t....

Can anyone point me in the right direction?? Thanks a lot

P.S. Can someone explain to me how to put in the cool math lettering, um I think it's called like latex or something...thanks again

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# Homework Help: Far out free response concerning motion

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