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Chapter 2: Problem 6
Is it possible to have zero velocity and still be accelerating?
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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, 3 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 part (a)'s average speed?
Starting from rest, an object undergoes acceleration given by \(a=b t,\) where \(t\) is time and \(b\) is a constant. Can you use \(b t\) for \(a\) in Equation 2.10 to predict the object's position as a function of time? Why or why not?
An object's position is given by \(x=b t+c t^{3},\) where \(b=1.50 \mathrm{m} / \mathrm{s}, c=0.640 \mathrm{m} / \mathrm{s}^{3},\) and \(t\) is time in seconds. To study the limiting process leading to the instantaneous velocity, calculate the object's average velocity over time intervals from (a) \(1.00 \mathrm{s}\) to \(3.00 \mathrm{s},\) (b) \(1.50 \mathrm{s}\) to \(2.50 \mathrm{s},\) and \((\mathrm{c}) 1.95 \mathrm{s}\) to \(2.05 \mathrm{s}.\) (d) Find the instantaneous velocity as a function of time by differentiating, and compare its value at 2 s with your average velocities.
In 2009, Usain Bolt of Jamaica set a world record in the 100-m dash with a time of 9.58 s. What was his average speed?
Under what conditions are average and instantaneous velocity equal?
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