Anonymous
Anonymous asked in Science & MathematicsPhysics · 1 month ago

Physics - Write an equation that describes the position x of a particle in relation to the time t?

A particle moves in a circle with a radius of 0.4 m, with a constant speed of 0.8 m/s.

Write an equation that gives x in relation to time t, supposing that in t=0, the particle is on the positive side of the x axis.

Can someone please explain the general equation for this type of problems?

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  • Whome
    Lv 7
    1 month ago
    Favourite answer

    A point on the rim of a wheel spinning with its axis at the origin casts a "shadow" on the x axis which is a sinusoidal function.

    As the point is moving a distance equal to two radii every second, we know that its angular velocity ω = 2 rad/s

    If we let the shadow be at its maximum excursion of 0.4 m at time zero, we are inclined to use a cosine function as cos0 = 1

    the general equation would be 

    x = Acos(ωt + φ)

    x = 0.4 cos(2t + φ)

    where φ is the phase shift and in this case could be any value 

    -π/2 < φ < π/2 keeping the x value positive when t = 0

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