(Solved): a. If an object is moving at a constant speed \( v \), then the time the object takes to traverse a ...

a. If an object is moving at a constant speed \( v \), then the time the object takes to traverse a distance \( \mathrm{d} \) is inversely proportional to its speed \( \mathrm{v} \). If it takes a car \( 1 \mathrm{~h} \) to travel a distance of \( 60 \mathrm{mi} \), how long will it take the car to travel the same distance if it slows down to onethird of its original speed? b. For a sound coming from a point source, the amplitude of sound is inversely proportional to the distance. If the displacement amplitude of an air molecule in a sound wave is \( 5.8 \mathrm{x} \) \( 10^{-6} \mathrm{~m} \) at a point \( 1.0 \mathrm{~m} \) from the source, what would be the displacement amplitude of the same sound when the distance increases to \( 6.0 \mathrm{~m} \) ? c. The gravitational force \( \mathrm{F} \) on an object is directly proportional to the object's mass. If the force on an object with \( m=2 \mathrm{~kg} \) is \( \mathrm{F}=9.8 \mathrm{~N} \), what is the force on an object with \( \mathrm{m}=3.8 \) \( \mathrm{Kg} \) ?