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how can an object that is oscillating have a 0 velocity

Mathematics
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it does have a velocity, really depends on which direction you are talking about
well i calculated the velocity of on object between 0 and pi, the equation i was given was .5cos(2t) t being time in seconds
does that make sense to you?

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Other answers:

Think of a pendulum. As it oscillates from one end to other, it changes direction. So the sign of velocity changes; so it has to be zero somewhere in between. To be specific the velocity is zero at the extremes and maximum in the middle

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