To find: The velocity after t seconds.
The velocity after t seconds is .
The equation of motion of a point on such a spring is .
(1) Constant Multiple Rule:
(2) Product Rule:
If is a displacement of a particle and the time t is in seconds, then the velocity of the particle is .
Obtain the velocity at time t.
Apply the product rule (2) and the constant multiple rule (1),
Therefore, the velocity after t seconds is .
To sketch: The position and velocity functions for
Using the online graphing calculator and the draw graph below shown in Figure 1.
From Figure 1, it is noticed that
(i) If is positive, then is an increasing function.
(ii) If is negative, then is a decreasing function.
(iii) If is local extreme (that is, local minimum or local maximum), then crosses the x-axis .
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