The motion of an object in one dimension can be plotted over time to make a position/time curve.

p(t) (meters)

The velocity of the object at time t, is the rate of change in the position, and is the slope of the position curve at time t. It can be plotted as a velocity over time curve.

v(t) = p'(t) (mtrs/sec)

The acceleration of the object at time t is the rate of change of the velocity, and is the slope of the velocity curve at time t. It can be plotted as an acceleration over time curve.

a(t) = v'(t) = p''(t) (mtrs/sec^{2})

In the interactive diagram above:

Move the green dots to reshape the position curve.

Move the blue line to see how the peaks, troughs, zero points, and inflection points line up.

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