# Thread: Maximum acceleration from velocity equation?

1. ## Maximum acceleration from velocity equation?

Hey guise,

I am asked to find the maximum acceleration of a rollercoaster that starts from rest and ends at 60 seconds, the horizontal acceleration is

a(t) = Cos(Pi/30t)

the velocity is v(t) = 30Sin(Pi/30t) + C

and I found out the displacement as s(t) = -900Cos(Pi/30t) + Ct

So given this, how do I find the max acceleration? Do I simply solve a(t) for 0? Which equation do I solve? I realize this is conceptual in some ways.

Granted, how would I solve for the maximum velocity? Total distance traveled? When the coasters are traveling at 150 meters/second?

2. ## Re: Maximum acceleration from velocity equation?

Hey guise,

I am asked to find the maximum acceleration of a rollercoaster that starts from rest and ends at 60 seconds, the horizontal acceleration is

a(t) = Cos(Pi/30t)

the velocity is v(t) = 30Sin(Pi/30t) + C

and I found out the displacement as s(t) = -900Cos(Pi/30t) + Ct

So given this, how do I find the max acceleration? Do I simply solve a(t) for 0? Which equation do I solve? I realize this is conceptual in some ways.

Granted, how would I solve for the maximum velocity? Total distance traveled? When the coasters are traveling at 150 meters/second?
What is the condition for local "maximum/minimum" of a function?

3. ## Re: Maximum acceleration from velocity equation?

Originally Posted by Subhotosh Khan
Hey guise,

I am asked to find the maximum acceleration of a rollercoaster that starts from rest and ends at 60 seconds, the horizontal acceleration is

a(t) = Cos(Pi/30t)

the velocity is v(t) = 30Sin(Pi/30t) + C

and I found out the displacement as s(t) = -900Cos(Pi/30t) + Ct

So given this, how do I find the max acceleration? Do I simply solve a(t) for 0? Which equation do I solve? I realize this is conceptual in some ways.

Granted, how would I solve for the maximum velocity? Total distance traveled? When the coasters are traveling at 150 meters/second?
What is the condition for local "maximum/minimum" of a function?
You set acceleration = 0 and figure values, and figure out whether values before or after than are positive or negative.

4. ## Re: Maximum acceleration from velocity equation?

Originally Posted by Subhotosh Khan
So given this, how do I find the max acceleration?
What is the condition for local "maximum/minimum" of a function?
You set acceleration = 0 and figure values, and figure out whether values before or after than are positive or negative.
Local maximum/minimum of a function f(x) is at points where the derivative of the function is equal to zero (df/dx = 0)

#### Posting Permissions

• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
•