Question

given info

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Tend = 1.31 s

Tmax= .654, Aamx= 66.7

The velocity is changing most rapidly at time

0.654

s

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information

Consider a one-dimensional acceleration that starts at zero at time zero, then increases to some maximum value, then decreases back to zero. Human pushing forces often create accelerations that fit this description; the pushing force is small when the hands of the human first make contact (assuming the fingertips touch first), large when the palms are flat against the object being pushed, and then small again as the fingertips are breaking contact with the object. This problem will ask you to find the resulting velocity and position equations for a particle subject to such an acceleration.

Assume that the object being accelerated is a cart that can roll without friction on a level floor. Also assume that the acceleration is always eastward, that the x axis has been chosen to be in the E-W direction with eastward positive, and that the x acceleration can be modeled by a quadratic equation

ax(t) = ( 204.0  cm/s3 )t − ( 156.0  cm/s4 )t2.

This equation is valid between time zero (when the acceleration is zero) and some time tend, when the acceleration is again zero. Also assume that, at time zero, the velocity of the rolling cart is 14.53550  cm/s WEST and that the position of the cart at time zero is chosen to be the origin.

1)What is the speed of the cart at time Tend?

2)At what instant of time (between time zero and time tend) is the position of the cart changing most rapidly?

3)At what instant of time (between time zero and time tend) is the cart farthest to the WEST of the origin?

4)What is the cart's distance from the origin at the location in time described in part G? This will be the cart's maximum distance to the WEST of the origin.

Answer 1