Question

1D Motion with Variable Acceleration K7 of 7> 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 az axis has been chosen to be in the E-W direction with eastward positive, and that the r acceleration can be modeled by a quadratic equation a()(2100 cm/s)t - (1680 em/s)t2 (168.0 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 13.67188 cm/s WEST and that the position of the cart at time zero is chosen to be the origin.

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

2. 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

2. 2 S