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'It's Only a Minus Sign' printed from http://nrich.maths.org/
In this problem we shall see how
a simple minus sign in a differential equation can completely
change the character of the solution.
Two particles are released from $x = 1$ at time $0$ and their speed
at any point x will be given by these two differential equations:
|particle $A \quad \quad$
Without solving the equations, can you describe how the
particles will move? Draw a sketch graph of the path you expect the
particles to take.
Now solve the equations to see if you were correct.
Next suppose that two more particles are released with a
positive velocity at time $0$ from the origin and move according to
these equations, in which v is the velocity of each particle:
|particle $C \quad \quad$
Without solving the equations, can you provide a clear
description of the subsequent motion of the particles?
Would releasing the particles with a negative velocity from the
origin have a significant effect on the type of motion which
Could you find initial starting points and velocities which would
give rise to motions in which the particles slow down and