"Rollercoasters" given equation find the following..

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Jaskaran

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May 5, 2006
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Hey all, I'm a calculus student but in need of a bit of a push here, the problem

"Each coaster starts starts from rest and lasts exactly sixty seconds. The horizontal accelerations (in meters/second^2) are given by

Coaster 1 \(\displaystyle a(t) = cos(Pi/30t)\)

Coaster 2 \(\displaystyle a(t) = t(t^2 - 3600)\)

Coaster 3 \(\displaystyle a(t) = 3t/[sqrt(4t+20)]\)

"Granted, please rank the given coasters in terms of 1) maximum acceleration 2) maximum velocity 3) total distance traveled. Finally, determine that time(s) at which each of the coasters is traveling at a rate of 150 meters/second. List any engineering flaws."

So my guess is that I need to take the anti-derivates of the a(t) for each rollercoaster? But when I do this, won't I end up with C, and in that case, how do I eliminate that variable?

Any amount of help is appreciated.
 
Jaskaran said:
Hey all, I'm a calculus student but in need of a bit of a push here, the problem

"Each coaster starts starts from rest and lasts exactly sixty seconds. The horizontal accelerations (in meters/second^2) are given by

Coaster 1 \(\displaystyle a(t) = cos(Pi/30t)\)

Coaster 2 \(\displaystyle a(t) = t(t^2 - 3600)\)

Coaster 3 \(\displaystyle a(t) = 3t/[sqrt(4t+20)]\)

"Granted, please rank the given coasters in terms of 1) maximum acceleration 2) maximum velocity 3) total distance traveled. Finally, determine that time(s) at which each of the coasters is traveling at a rate of 150 meters/second. List any engineering flaws."

So my guess is that I need to take the anti-derivates of the a(t) for each rollercoaster? But when I do this, won't I end up with C, and in that case, how do I eliminate that variable?

Any amount of help is appreciated.
Click to expand...

You are given initial and final conditions - that would eliminate the constants.
 
Thank you, I thought about that.

I've figured out the anti-derivatives (velocity and displacement) for the first two, but how do I figure it out for the third rollercoaster? :?

What methods of integration would work?

And finally, to find the max acceleration, I have to solve for velocity at 0???

Also, how do I find the displacement? What will be inside the absolute values? Anyway to solve this without the use of a graphic calculator?
 
Jaskaran said:
Thank you, I thought about that.

I've figured out the anti-derivatives (velocity and displacement) for the first two, but how do I figure it out for the third rollercoaster? :?

What methods of integration would work?

And finally, to find the max acceleration, I have to solve for velocity at 0???

Also, how do I find the displacement? What will be inside the absolute values? Anyway to solve this without the use of a graphic calculator?
Click to expand...

For #3 - I would use substitution:

u = t+5
Sure - you can do these without graphing calculator. If you have excel in your computer - you can graph all these.
 
How'd you get t+5 for u-sub? :?

Also, thanks a lot for these, could u give me through one complete example if it's not too much? :oops:
 
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