blike Posted February 6, 2003 Share Posted February 6, 2003 What exactly does instantaneous velocity mean? Link to comment Share on other sites More sharing options...
fafalone Posted February 6, 2003 Share Posted February 6, 2003 The velocity at any given point. The average velocity is for the entire period of motion; i.e. when I drove from Sarasota to Miami in 2.3 hours, my average velocity was 206/2.3 = 89.56mph; but this doesn't reflect that my velocity was 80mph when I was picking something up on my radar detector and going 100 when I wasn't. Instantaneous velocity is the value of the derivative of the position vector at any given moment, independent of :delta:t Say the equation describing my position was 2t^2. My average velocity between 0 and 10 is 400/10 = 40. My velocity at 5 seconds, d/dt = 4t, is 20. Link to comment Share on other sites More sharing options...
blike Posted February 7, 2003 Author Share Posted February 7, 2003 ok quick question: in your example you gave the equation 2t^2. do you mean 2(t^2) or (2t)^2? if you meant the first equation [which i'm assuming you did] wouldn't your average velocity be 200/10 or 20... but what would the derivative of (2t)^2 be? EDIT: eh, disregard that. (2t)^2 => 4t^2 which would be 8t Link to comment Share on other sites More sharing options...
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