A mass attached to spring oscillates block and forth as indicated in the positio

Question

A mass attached to spring oscillates block and forth as indicated in the position vs. time plot below. At point P The x-component of the velocity is negative and the x-component of the acceleration is positive The x-component of the velocity is negative and the x-component of the acceleration is negative The x-component of the velocity is zero and the x-component of the acceleration is not zero The x-component of the velocity is positive and the x-component of the acceleration is positive The x-component of the velocity is positive and the x-component of the acceleration is negative

Explanation / Answer

velocity = dx/dt = slope of curve
acceleration = d2x/dt2 = d(dx/dt)/dt = slope of the derivative of the function

Lets say that x = cos t
so dx/dt = - sin t
d2x/dt2 = - cos t

t is now in (3*pi/2, 2*pi)
So velocity in this set will be -sint = -1 * (negative value) =  positive
acc = - cost = -1 * (positive value) = negative

Last option is correct

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