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A particle moves with constant speed of 3m/sec along path y=3x^2
What is the acceleration of the particle at x=1.5m?

  • physics -

    Since the speed is constant, the acceleration must be caused by the change in direction. The angle of the trajectory to the x axis is
    theta = arctan (dy/dx) = arctan (6x)
    When x = 1.5, theta = arctan 9 = 83.66 degrees
    The acceleration will be
    (speed)x d(theta)/dt
    = (speed)* d(theta)/dx* dx/dt

    Take it from there.

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