dx/dt is the symbol for change in position along X (dx) over some small period of time (dt). Thus, whenever the change in position is a net zero in the time period dt, we have dx = 0 over dt > 0 and dx/dt = 0/T; where T is some small passage of time or dt. Thus, v(x) = dx/dt = 0/T = 0 and velocity in the X direction is zero.
Here's an example. You step forward one foot; then immediately return to where you started from. The fore/aft stepping takes a second; so T = dt = 1 sec. In that one second, you went dx = x0 - x1 feet; where x0 = 1 foot forward and x1 = 1 foot back. Thus, dx = 1 - 1 = 0. So we have v(x) = dx/dt = 0 feet/1 sec = 0 feet/sec.
The X distance is a vector, it has direction (fore and aft) and magnitude (one foot). Thus going forward and backward one foot each cancel out to give us dx = 0 over that one second of motion.
Of course, another way dx = 0, is for something to be static. That is, it does not move over time. In which case, dx/dt = 0/T simply because whatever you are measuring is not displaced over time at all.
2007-07-28 20:26:08
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answer #1
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answered by oldprof 7
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velocity is the derivative of displacement right??? so if ur asked to find the derivative of say...a constant...like 5...then the derivative is zero. so if x is a constant, then your velocity will be zero
2007-08-01 05:28:33
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answer #2
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answered by Anonymous
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the displacement (x) must be zero during the interval of time.
2007-07-28 20:33:46
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answer #3
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answered by aryabhatt 1
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the displacement (x) must be zero during the interval of time.
2007-07-28 20:10:31
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answer #4
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answered by jim 3
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its very very very very very simple the object must be @ rest or the forces applied on the object should be equal on all the sides
2007-07-29 00:28:09
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answer #5
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answered by NIVEDHA P 2
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That x is not changing.
2007-07-28 20:05:58
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answer #6
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answered by Anonymous
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You need pie. No pi, PIE.
2007-07-28 20:05:20
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answer #7
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answered by Just_One_Man's_Opinion 5
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s is constant
2007-07-29 01:19:12
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answer #8
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answered by kaushik patel 2
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