IlluminatingBikr
Flashlight Enthusiast
- Joined
- Feb 26, 2003
- Messages
- 2,320
Well doesn't that just sound like fun?
Okay so for calculus we have been working on this project. It's totally fine if we get help with it, but we just have to understand the work and actually be able to do it ourselves.
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You are a local bicycle racing star and today you are in the race of your life. Moving at a constant velocity "k" meters per second, you pass a refreshment station. At that instant (t=0 seconds) your support car starts from the refreshment station to accelerate after you, beginning from a dead stop. Suppose the distance traveled by you in t seconds is given by the expression kt and distance traveled by the support car is given by the function (1/3)*(12t^2-t^3), where distance is measured in meters. This latter function is carefully calculated by your crew so that at the instant the car catches up to you, they will match speeds. A crew member will hand you a cold drink and the car will immediately fall behind.
a.) How long odes it take the support car to catch up to you?
t = 6 seconds
b.) How fast are you traveling
k = 12 meters/second
c.) Suppose that you are riding at a constant velocity k, which may be different than the value found in part (a). Find an expression for the times when the car and the bike meet which gives these times as a function of your velocity k. (In other words, solve for t in terms of k and simplify).
How many times would the car and the bike meet if you were going faster than the velocity found in part (a)?
How many times would the car and the bike meet if you were going slower than the velocity found in part (a)?
Show by example.
d.) Consider a pair of axes with time measured horizontally and distance vertically. Draw graphs that depict the distance traveled by you and by the car plotted on the same axes for the original problem (parts (a) and (b)) and for the questions of part (c). You should have three graphs: one for the bike's velocity found in part (a), one for a faster bike, and one for a slower bike (use the velocities you used for examples from part (c).
If you had been going any faster or slower than the velocity you found in part (a), passing the drink would not have been so easy. Why? Justify your answer.
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I have already computed parts a and b to be 6 seconds and 12 meters/second, respectively.
I have been trying to solve for time in terms of k, (as per part c) and I get stuck with 3k = 12t - t^2. I have a t and t^2 term, and I'm not sure how to solve this. Any advice?
Okay so for calculus we have been working on this project. It's totally fine if we get help with it, but we just have to understand the work and actually be able to do it ourselves.
******************
You are a local bicycle racing star and today you are in the race of your life. Moving at a constant velocity "k" meters per second, you pass a refreshment station. At that instant (t=0 seconds) your support car starts from the refreshment station to accelerate after you, beginning from a dead stop. Suppose the distance traveled by you in t seconds is given by the expression kt and distance traveled by the support car is given by the function (1/3)*(12t^2-t^3), where distance is measured in meters. This latter function is carefully calculated by your crew so that at the instant the car catches up to you, they will match speeds. A crew member will hand you a cold drink and the car will immediately fall behind.
a.) How long odes it take the support car to catch up to you?
t = 6 seconds
b.) How fast are you traveling
k = 12 meters/second
c.) Suppose that you are riding at a constant velocity k, which may be different than the value found in part (a). Find an expression for the times when the car and the bike meet which gives these times as a function of your velocity k. (In other words, solve for t in terms of k and simplify).
How many times would the car and the bike meet if you were going faster than the velocity found in part (a)?
How many times would the car and the bike meet if you were going slower than the velocity found in part (a)?
Show by example.
d.) Consider a pair of axes with time measured horizontally and distance vertically. Draw graphs that depict the distance traveled by you and by the car plotted on the same axes for the original problem (parts (a) and (b)) and for the questions of part (c). You should have three graphs: one for the bike's velocity found in part (a), one for a faster bike, and one for a slower bike (use the velocities you used for examples from part (c).
If you had been going any faster or slower than the velocity you found in part (a), passing the drink would not have been so easy. Why? Justify your answer.
******************
I have already computed parts a and b to be 6 seconds and 12 meters/second, respectively.
I have been trying to solve for time in terms of k, (as per part c) and I get stuck with 3k = 12t - t^2. I have a t and t^2 term, and I'm not sure how to solve this. Any advice?
