Overview
Two cars, black and red, compete in a drag race. In this drag race, each car starts from rest at the same instant, speeds up to its maximum velocity, then continues at maximum velocity until it crosses the finish line. Neither car slows down, or stops, during the race. Of course, both cars will stop sometime after crossing the finish line, but anything that happens after the finish line is outside this assignment. (1) RNG: Choose random maximum velocities (60-90 m/s) and accelerations (10-14 m/s2 ) for the two cars: the red car's maximum velocity must be at least 10 m/s higher than the black car's, and the black car's acceleration must be at least 2 m/s2 higher than the red car's. No calculations, just list your four randoms by description and symbol (vB, vR, aB, aR). (2) Since the black car has a higher acceleration, it will initially pull ahead. Calculate the distance between the cars (how far ahead the black car is) at the instant the black car reaches maximum velocity. (3) Calculate the distance between the cars at the instant the red car reaches maximum velocity. (4) The red car will eventually pass the black car and win the race. But does the red car catch up with the black car before or after the red car reaches its maximum velocity? Explain how you can tell, in 1-2 sentences, solely based on the calculations done in #3. No new calculations - this question is explanation-only. (5) The race track is 2.00 km long. Prove that the red car wins the race by calculating the total time for each car to reach the finish line. Tips: Don't use any of the equations for average speed, velocity, or acceleration. Remember that the 1D kinematics equations of motion only work for intervals with constant acceleration, and in this race, the acceleration of each car changes (to … ?) at the instant it reaches maximum velocity. You can't assume that the cars reach maximum velocity at the halfway point. Where that occurs for each car is up to you to discover. Organization: Make your solutions to each question as easy to follow as you can: break them into sections with headings, identify which car and which interval you're working on, identify every quantity you calculate. Sketches may help you keep things straight, but are not required to be in the solution. And always begin work with eqns from the eqn sheet, using subscripts to avoid confusion.