Chapter 2: Problem 2
Does a speedometer measure speed or velocity?
Chapter 2: Problem 2
Does a speedometer measure speed or velocity?
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Get started for freeIce skaters, ballet dancers, and basketball players executing vertical leaps often give the illusion of "hanging" almost motionless near the top of the leap. To see why this is, consider a leap to maximum height \(h .\) Of the total time spent in the air, what fraction is spent in the upper half (i.e., at \(y>\frac{1}{2} h\) )?
The standard 26 -mile, 385 -yard marathon dates to \(1908,\) when the Olympic marathon started at Windsor Castle and finished before the Royal Box at London's Olympic Stadium. Today's top marathoners achieve times around 2 hours, 4 minutes for the standard marathon. (a) What's the average speed of a marathon run in this time? (b) Marathons before 1908 were typically about 25 miles. How much longer does the race last today as a result of the extra mile and 385 yards, assuming it's run at the average speed?
A balloon is rising at \(10 \mathrm{m} / \mathrm{s}\) when its passenger throws a ball straight up at \(12 \mathrm{m} / \mathrm{s}\) relative to the balloon. How much later does the passenger catch the ball?
An object's position is given by \(x=b t^{3},\) with \(x\) in meters, \(t\) in seconds, and \(b=1.5 \mathrm{m} / \mathrm{s}^{3} .\) Determine (a) the instantaneous velocity and (b) the instantaneous acceleration at the end of \(2.5 \mathrm{s}\) Find (c) the average velocity and (d) the average acceleration during the first \(2.5 \mathrm{s}\)
A racing car undergoing constant acceleration covers \(140 \mathrm{m}\) in 3.6 s. (a) If it's moving at \(53 \mathrm{m} / \mathrm{s}\) at the end of this interval, what was its speed at the beginning of the interval? (b) How far did it travel from rest to the end of the 140 -m distance?
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