- A drag race, commonly called a pass, is run on a 1320ft (¼ mile) long track. Suppose a dragster finishes a pass in ten seconds. How fast was the dragster going?
- Suppose we know that this same dragster travelled 285ft in the first five seconds of the pass. What was its average speed of the dragster for the first half of the race? What was its average speed of the dragster for the second half of the race?
- Suppose we have a model for how far \(d\) the dragster has travelled from the starting line for any time \(t\) between zero and ten seconds after it started the pass, and that model for the distance is given by a function \(f\) of time as \[ d \;=\; f(t) = t^3 + 32t\,. \] How fast was the dragster going exactly five seconds into the pass?
- Suppose a dragster starts a 1320ft pass at a constant speed of 6ft/s. After five seconds the dragster enters a wormhole and is instantly transported to a position 30ft from the finish line, from where it continues at a constant speed of 6ft/s, finishing the pass in ten seconds. What was the average speed of the dragster during this pass?
The Full Prompt
A drag race, commonly called a pass, is run on a \(1320\) ft (¼ mile) long track. Suppose we have a model for how far \(d\) the dragster has travelled from the starting line for any time \(t\) after it started the pass until \({t=10}\) seconds when it crossed the finish line, and that model for the distance is given by a function \(f\) of time as \[ d \;=\; f(t) = t^3 + 32t\,. \] How fast was the dragster going exactly five seconds into the pass?