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29 May, 08:17

At one instant a bicyclist is 40.0 m due east of a park's flag - pole, going due south with a speed of 10.0 m/s. then 30.0 s later, the cyclist is 40.0 m due north of the flagpole, going due east with a speed of 10.0 m/s. for the cyclist in this 30.0 s interval, what are the (a) magnitude and (b) direction of the displacement, the (c) magni - tude and (d) direction of the average velocity, and the (e) magni - tude and (f) direction of the average acceleration?

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  1. 29 May, 10:18
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    consider the east-west direction along the x-direction and north-south direction along the y-axis

    a)

    x₁ = initial position = 40 i + 0 j

    x₂ = final position = 0 i + 40 j

    displacement is given as

    Δx = x₂ - x₁ = (0 i + 40 j) - (40 i + 0 j) = - 40 i + 40 j

    magnitude : sqrt (( - 40) ² + (40) ²) = 56.6 m

    b)

    direction : 180 - tan⁻¹ (40/40) = 135 deg counterclockwise from east

    c)

    average velocity is given as

    average velocity = displacemen/time

    average velocity = ( - 40 i + 40 j) / 30 = - 1.33 i + 1.33 j

    magnitude : sqrt (( - 1.33) ² + (1.33) ²) = 1.88 m/s

    d)

    direction : direction : 180 - tan⁻¹ (1.33/1.33) = 135 deg counterclockwise from east

    e)

    v₁ = initial velocity = - 10 j

    v₂ = final velocity = 10 i

    average acceleration is given as

    a = (v₂ - v₁) / t = (10 i - 10 j) / 30 = 0.33 i - 0.33 j

    magnitude : sqrt ((0.33) ² + ( - 0.33) ²) = 0.47 m/s

    f)

    direction : direction : 360 - tan⁻¹ (0.33/0.33) = 315 counterclockwise from east
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