Maximum acceleration from velocity equation?

[Jaskaran]

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?

 

[Deleted member 4993]

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?

 

[Jaskaran]

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.

 

[Deleted member 4993]

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)