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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.

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 allow you 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?

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.

For sketched graphs, you needn't put numbers on the axes, even though we did that for the position graph here. It is important, however, that you make your time axes consistent with each other. In this case, at the second division of the time axis, the velocity goes to zero. Thus, on the position graph we expect to see the position's slope at zero (which it is). Graders will always check for this kind of consistency.

Note that the peaks of the velocity (solid dark red graph) do not occur at the same time as the position (dotted blue graph) peaks! Rather, they correspond to changes in the curvature of the position graph.