A weight is hung from a spring and set in motion so that it moves up and down continuously. The velocity v of the weight at any time t is gi

Question

A weight is hung from a spring and set in motion so that it moves up and down continuously. The velocity v of the weight at any time t is given by the equation v = 1.5 cos(4πt) where v is measured in meters per second and t is measured in seconds. Find the maximum velocity of the weight and the amount of time it takes for the weight to move from its lowest position to its highest position.

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Nevaeh 2 months 2021-10-14T22:13:43+00:00 1 Answer 0 views 0

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    2021-10-14T22:14:51+00:00

    Answer:

    0.25s

    Step-by-step explanation:

    As v = 1.5 cos(4πt), v is maximum when cos(4πt) is maximum = 1. So the maximum velocity would be 1.5 m/s

    Both the lowest and highest position occurs when its derivative is 0, aka v = 0 and has a change of direction

    1.5 cos(4πt) = 0

    cos(4πt) = 0

    4πt = π/2 and 4πt = 3π/2

    t = 1/8 = 0.125s and t = 3/8 = 0.375s

    So the time it takes to travels from 1 point of time (0.125s) to another point of time (0.375) is

    \Delta t = 0.375 - 0.125 = 0.25s

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