A car of mass m accelerates from rest along a level straighttrack, not at constant acceleration but with constant engine power,P. Assume that air resistance is negligible.
(a) Find the car's velocity as a function of time.
(b) A second car starts from rest alongside the first car on thesame track, but maintains constant acceleration. Which car takesthe initial lead? Does the other car overtake it? If yes, write aformula for the distance from the starting point at which thishappens.
(c) You are in a drag race, on a straight level track, with anopponent whose car maintains a constant acceleration of 12m/s2. Both cars have identical masses of 1000 kg. Thecars start together from rest. Air resistance is assumed to benegligible. Calculate the minimum power your engine needs for youto win the race, assuming the power output is constant and thedistance to finish line is 0.250 mi.
A car of mass m accelerates from rest along a level straighttrack, not at constant acceleration but with constant engine power,P. Assume that air resistance is negligible.
(a) Find the car's velocity as a function of time.
(b) A second car starts from rest alongside the first car on thesame track, but maintains constant acceleration. Which car takesthe initial lead? Does the other car overtake it? If yes, write aformula for the distance from the starting point at which thishappens.
(c) You are in a drag race, on a straight level track, with anopponent whose car maintains a constant acceleration of 12m/s2. Both cars have identical masses of 1000 kg. Thecars start together from rest. Air resistance is assumed to benegligible. Calculate the minimum power your engine needs for youto win the race, assuming the power output is constant and thedistance to finish line is 0.250 mi.
