The height at time t of a small weight oscillating at the end of a spring is .5cos(8t). How can I find the average velocity over the time intervals [3,4], [3,3.5], [3,3.1]? How can i find the weights instantaneous velocity at time t = 3?
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Originally Posted by colerelm1 The height at time t of a small weight oscillating at the end of a spring is .5cos(8t). How can I find the average velocity over the time intervals [3,4], [3,3.5], [3,3.1]? How can i find the weights instantaneous velocity at time t = 3? You're expected to know and apply the following: The average rate of change of a function f(x) over the interval [a, b] is given by The instantaneous rate of change of a function at x = a is where is the derivative of the function.
avg velocity = displacement/time taken. so over the interval [3,4] avg velocity = (0.5cos(8*4)-0.5cos(8*3))/(4-3). rest can be done in the same way. for instantaneous velocity just differentiate the function 0.5cos(8t). put t=3 in the derived function.
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