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'Phase Space' printed from http://nrich.maths.org/
A particle moves in a straight line under the action of a unknown
force and its motion is observed in various situations.
The position $x$ of the particle is plotted against its velocity
$v$ for the motion in the following 6 cases.
In each case, what can you say about the motion of the
In which way does each travel along the curve?
Can you think of a plausible physical interpretation for
What can you deduce about points corresponding to equal time
intervals of the motion?
Next consider the velocity-position diagrams for the following
1. A rubber ball dropped perpendicular to a hard concrete floor (if
you know about coefficients of restitution, you could draw this
motion accurately for $e=0.7$, neglecting all friction and air
2. A large parcel dropped from a stationary and very high
3. An air hockey puck struck hard and perpendicular to a side on an
air hockey table.
generally about the meaning of velocity-position diagrams and the
relationship to speed-time diagrams.