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15 October, 20:43

A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 1 2 and t = 1 s? Use Galileo's formula v (t) = - 9.8t m/s.

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  1. 15 October, 23:00
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    There is one mistake in the question. The Correct question is here

    A cat falls from a tree (with zero initial velocity) at time t = 0. How far does the cat fall between t = 1/2 and t = 1 s? Use Galileo's formula v (t) = - 9.8t m/s.

    Answer:

    y (1s) - y (1/2s) = - 3.675 m

    The cat falls 3.675 m between time 1/2 s and 1 s.

    Explanation:

    Given data

    time=1/2 sec to 1 sec

    v (t) = -9.8t m/s

    To find

    Distance

    Solution

    As the acceleration as first derivative of velocity with respect to time

    So

    acceleration (-g) = dv/dt

    Solve it

    dv = a dt

    dv = - g dt

    v - v₀ = - gt

    v = dy/dt

    dy = v dt

    dy = (v₀ - gt) dt

    y (1s) - y (1/2s) = (v₀) (1 - 1/2) - (g/2) [ (t1) ² - (t1/2s) ² ]

    y (1s) - y (1/2s) = ( - 9.8/2) [ (1) ² - (1/2) ² ]

    y1s - y1/2s = ( - 4.9 m/s²) (3/4 s²)

    y (1s) - y (1/2s) = - 3.675 m

    The cat falls 3.675 m between time 1/2 s and 1 s.
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