A meteor approaching the atmosphere was estimated to have a speed function of s(t) = 432 - 7.5t, where s is the speed in m / sec and time t is the time in seconds since the meteor was at a specified point in space.
The goal is to use the speed function to determine the distance traveled by the meteor in the first 30 seconds since the meteor was at the specified point. We will estimate this net change in distance using the speed function.
1) First estimate:
Use time intervals 10 seconds long. For each interval, assume a constant speed equal to the actual speed at the starting time (left side) of each interval.
1 a) Sketch, on the graph below, the function you'll be using to complete #1. (Based on set-up above)
1 b) Predict whether this estimate will lb) Predict whether this estimate will Explain why. (This has nothing to do with area!)
1 c) Use your pretend speed functions to approximate the distance traveled by the meteor in this 30 sec period.
2) Second estimate:
Use time intervals 10 seconds long. For each interval, assume a constant speed equal to the true speed at the ending time (right side) of each interval.
2 a) Sketch, on the graph below, the function you'll be using to complete #2. (Based on set-up above)
2 b) Predict whether this estimate will be an under-estimate or an over estimate.
2 c) Find an approximate distance traveled. Show work!
3) Third estimate:
Use time intervals 6 seconds long. For each interval, assume a constant speed equal to the actual speed at the starting time (left side) of each interval.
3 a) Sketch, on the graph below, the function you'll be using to complete #3. (Based on set-up above)
3b) Estimate the dist traveled. Show work!
4) Fourth estimate: (Read carefully!) Use 6 intervals, of equal time length. For each interval, assume a constant speed equal to the true speed at the ending time (right side) of each interval.
4 a) Sketch, on the graph below, the function you'll be using to complete #4. (based on set-up above)
4 b) Estimate the dist traveled. Show work!
5) Which of the four estimates is closest to the actual distance traveled by the meteor in 30 seconds? Explain your reasoning.
6) Write an expression using s (t) that represents the actual distance traveled by the meteor in the first 30 seconds:
7) Evaluate your expression using the Fundamental Theorem, to find the actual distance traveled. Show all work.