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Nit pick?: You mean crossing the zero line? Dipping implies a concave line.
bc, who hopes the debate will recommence.
p.s. are we to imagine no dissipation?
if I drive a car up a slope then engage neutral,
the car slows and reverses, back down the slope.
The velocity is graphed by a straight line slope, dropping through
zero at the car's high point.
The acceleration on such a graph would be a straight
horizontal line. That is, it is non-zero, when the velocity
goes through zero.
Now consider the case when I drive forward, coast to a standstill,
and at the moment the speed is zero, I apply the brake.
What is the physical significance of the acceleration dropping
suddenly to zero?