# PS.1.4 Sketch the Motion

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A particle of mass $$\displaystyle m$$ is moving along the +$$\displaystyle x$$-axis with a constant speed $$\displaystyle v_0$$. At time $$\displaystyle t = 0$$ it enters a region in space between two parallel plates which are separated by a distance $$\displaystyle h$$ and are contained in the $$\displaystyle x$$-$$\displaystyle z$$ plane. The figure shows a side view of the plates, the +$$\displaystyle z$$ axis is out of the screen. While the particle is between the plates, it is acted on by both gravity and by a time varying force that points upward (along the +$$\displaystyle y$$-direction) and has magnitude $$\displaystyle F = bt$$, where $$\displaystyle b$$ is a positive constant that is sufficiently large such that the particle hits the top plate without ever touching the bottom plate.

(Part 1) What are the units of the constant $$\displaystyle b$$? Enter m for meters, s for seconds and kg for kilograms. Make a sketch of what you think the trajectory of the particle is as it moves through the plates. Draw a coordinate system showing the position of the particle at time $$\displaystyle t$$. Clearly indicate your origin, choice of axis, and draw in the coordinate functions for the position of the particle at time $$\displaystyle t$$?

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