anonymous
  • anonymous
If the position of a particle at time t is given by S(t)=t^3, find: a.) the average velocity, v5, 5.1 between times t=5 and t=5.1. b.) the average velocity, v5, 5.01 between times t=5 and t=5.01. c.) Using the above, estimate the instantaneous velocity v(5). Note: (5.1)^3=132.651 and (5.01)^3=125.751501
Mathematics
jamiebookeater
  • jamiebookeater
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nenadmatematika
  • nenadmatematika
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anonymous
  • anonymous
So, how would the last part (c), finally look? I got a&b.
anonymous
  • anonymous
Would it be 75?

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nenadmatematika
  • nenadmatematika
yes 75 is the answer, derivative of t^3 is 3t^2...plug in t=5 and you'll get 75, but the thing is, in your task they want to feel the derivative...what happens to the slope of the secant line when you approach to 5...secant becomes tangent...

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