Worksheet 5 Math 1261. Suppose a train follows a circular path of radiusRat constant speed. Compute theacceleration, and show that it is perpendicular to the direction of travel of the trainand points into the circle.2. Engineers in France observed that high–speed trains will not stay on the tracks if thetracks are constructed of straight lines and arcs of circles. Use the answer to problem1 to explain why the trains will tend to leave the tracks at the juncture of a straighttrack and a circular track.Remark:If the acceleration of a vehicle changes abruptly, the passengers will feela sudden push in the opposite direction.For instance, if the driver steps on theaccelerator, you will be pushed backwards in your seat. Perhaps you have also felt asideways jolt when riding in a train or car.3. Suppose we want the train to make a smooth transition from a straight track alongthe liney=-xforx≤ -1 to a straight track along the liney=xforx≥1. That is,we seek a new curve (x, y(x
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