these times as a function of her? Carol is a local bicycle racing star and today she is in the race of her life. Moving at a constant velocity k meters per second, she passes a refreshment station. At that instant (t=0), her support car starts from the refreshment station to accelerate after her, beginning from a dead stop. Suppose the distance traveled by Carol in t seconds is given by d(t)=kt and distance traveled by the support car is given by the function d(t)=(1/3)(10t^2-t^3), where distance is measured in meters. This latter function is carefully calculated by her crew so that at the instant the car catches up to the racer, they will match speeds. A crew member will hand Carol a cold drink and the car will immediately fall behind.
C. Suppose that Carol is riding at a constant velocity k. Find an expression for the times when the car and the bike meet which gives these times as a function of her velocity k. How many times would the car and the bike meet if Carol were going faster than t^2-10t+3k? Slower?
C. Suppose that Carol is riding at a constant velocity k. Find an expression for the times when the car and the bike meet which gives these times as a function of her velocity k. How many times would the car and the bike meet if Carol were going faster than t^2-10t+3k? Slower?