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A particle projected from the origin (x = y = 0) moves in xy plane with a velocity v = 2i ^ + 4xj ^, where i ^ & j ^ are the unit vectors along x and y axis. The equation of the motion of the particle is– (a) y = x2 (b) y = 2x2 (c) y = x^2/2 (d) y = x^2/4

A particle projected from the origin (x = y = 0) moves in xy plane with a velocity v = 2i ^ + 4xj ^, where i ^ & j ^ are the unit vectors along x and y axis. The equation of the motion of the particle is–
    (a)    y = x2
    (b)    y = 2x2
    (c)    y = x^2/2
    (d)    y = x^2/4

Grade:upto college level

1 Answers

Simran Bhatia
348 Points
9 years ago

(a)

    v = 2i ^+4xj ^, v = v_x i ^+v_y j ^

    vx = 2, vy = 4x

    dy/dt=dy/dx=dx/dt

    4x = dy/dx.2

    Integrating, y = 2 x^2/2 = x2

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