6. A rocket burning its onboard fuel while moving through space has velocity −→v (t) and mass m(t) at time t. If the exhaust gases escape with velocity −→v e, relative to the rocket, then md−→v /dt = dm/dt−→v e. (a) Show using this equation that −→v (t) = −→v (0) − ln(m(0)/m(t))−→v e; (b) If the rocket accelerates in a straight line from rest to twice the speed of its exhaust gases, then what fraction of its initial mass would the rocket have to burn as fuel?

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it's when something is going so fast it makes a loud noise, breaking the sound barrier, for example: a jet makes a loud noise, not only cause of the jet but because they reached a point where they went so fast that you can year the noise from various parts, kinda like a police car, lets say the car was going   so fast that you hear the siren of the cop car right next to you, but the car is probably a mile a way, it's cos the siren was next to you a few seconds if you understand me