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Approach: Once the fan has been reversed, the acceleration is in the opposite direction from the velocity. Thus, the boat will immediately begin to slow down. As it slows, it will continue to move east, however. In the language of our one-dimensional system, the velocity immediately begins to decrease with time, but the position continues to increase until the instant that the velocity has decreased to zero.
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It is very tempting to assume that as soon as the fan is reversed, the boat begins to move backward. This is not the case, however. Consider the case of a commercial jet, landing at over 100 mph. The pilots will usually reverse the engines within a few seconds of landing to help slow the plane. If the plane were to immediately reverse direction, the effect on the passengers would be as if it had hit a brick wall and bounced off! Instead, the plane continues along the runway while gently decreasing its speed. |
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One of the (many) reasons that your intuition might tell you that reversing the engine immediately reverses the direction is experience operating automobiles. In a car, the transmission is not designed to reverse the engine to slow the car. When the engine is in reverse either the car is moving backward or you are about to spend a few thousand dollars on your transmission. What feature do cars have (that is not present on the air/ice boat) to compensate for the fact that the engine cannot produce a significant acceleration in the direction opposite the car's motion? |
The motion is not finished when the boat stops, however. If the fan is left in reverse, the continued thrust will now begin to accelerate the boat backward. In one-dimensional language, the velocity reaches zero and continues to decrease, so the speed (absolute value of velocity) is now increasing. The boat will therefore begin to move west, and with increasing speed. Thus, the position vs. time graph will begin to decrease with a steepening slope.
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It is vitally important to remember that an object cannot remain at rest for more than an instant if it is acted upon by a constant acceleration. |
B.) Sketch rough graphs of your position and velocity as a function of time from the instant the fan was reversed.
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