The black carriage has a vertical slot that is driven in an oscillatory manner.

Question

The black carriage has a vertical slot that is driven in an oscillatory manner. The carriage position x(t) as a function of time is x = 3 sin( 2 t) , where x is in cm and t is in seconds. This carriage in turn drives the motion of pin A which is further constrained to move in the parabolic slot (white curve) whose shape is described by the function y = -x^2, where the y-coordinate also has units of cm. Determine the overall velocity of pin A as a function of time t. A particle moves on a plane with a velocity of v(t) = (5t i bar - t^2 j bar) cm/s. if the particle's initial position is r bar_0 = (i bar + j bar) cm at t0 = 0 . Calculate the displacement, average velocity, average acceleration and total distance traveled between 0 and 10 seconds.

Explanation / Answer

4)   Given:    x = 3 sin(3t) cm and   y = -x 2 cm

Find: v = vx i + vy j

Now r = x i + y j and v = dr/dt = (x dot)i + (y dot)j

vx = dx/dt = d(3 sin 2t)/dt = 6 cos2t

vy = dy/dt = (dy/dx).(dx/dt) = (-2x).(6 cos2t)= -36 sin2t.cos2t

so, v = vx i + vy j = 6 cos2t i - 36 sin2t.cos2t j cm/s

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