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Chapter 2: Problem 5
Is it possible to be at position \(x=0\) and still be moving?
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A subway train is stalled in a station. A second train approaches the station at \(61.2 \mathrm{~km} / \mathrm{h}\) and brakes to a halt in \(37.6 \mathrm{~s}\), stopping just \(1.35 \mathrm{~m}\) short of the stalled train. What was the distance between the two trains at the instant the moving train began to brake?
In a \(400-\mathrm{m}\) drag race, two cars start at the same time, and each maintains a constant acceleration. The winner's acceleration is \(4.25 \mathrm{~m} / \mathrm{s}^{2}\), and the winner reaches the finish line \(248 \mathrm{~ms}\) before the loser does. By what distance is the loser behind when the winner reaches the finish line?
Under what conditions are average and instantaneous velocity equal?
You're a consultant on a movie set, and the producer wants a car to drop so that it crosses the camera's field of view in time \(\Delta t\). The field of view has height \(h\). Derive an expression for the height above the top of the field of view from which the car should be released.
In 2014 the Philae spacecraft became the first artifact to land on a comet. Unfortunately, Philae bounced off the comet's surface and ultimately landed in a nonideal location. After its first contact, Philae was moving upward at \(38 \mathrm{~cm} / \mathrm{s}\), and it rose to a maximum height of about \(1 \mathrm{~km}\). Estimate the gravitational acceleration of the comet, assuming it's constant (not a very good assumption in this case).
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