Particle motion - Path Coordinates

[Alexanddros81]

Homework Statement

Pytel Dynamics Problem 13.4

13.4 The particle passespoint O at the speed of 2.4 m/s. Between O and B, the speed changes
at the rate of 2.2√v m/s², where v is the speed in m/s. Determine the magnitude of
the acceleration when the particle is (a) just to the left of pont A; and (b) just to right of point A.

Homework Equations

The Attempt at a Solution

He gives solutions for a) 4.145 m/s². I get the following:

for b) he gives 6.690 m/s²

My problem is how to solve part b. I have done trial and error by using the equation
v²/2=a_ts+C but I don't know what assumptions should I make.

 

[Funky_Sp]

At the right side of point A , the particle begins to rotate so you need to take that to consideration.

 

[Alexanddros81]

At the right point of A do I say v=3.65 m/s, a_t = ? and s=0 or 0.9?
Am I looking to find a=√(a_t)² + (a_n)² ?

 

[Funky_Sp]

You can see the problem at the right side of A as following. A particle with initial speed and initial acceleration starts a rotation.
I would suggest you to begin from the definition of the angular acceleration. If you set s=0 is fine.

 

[Alexanddros81]

Some more help...
I tried some different things but no luck.
I have set s=0 and v = 3.65 to equation v²/2=a_ts+C and found C=6.661
Also I have found a_n just after A to be 5.55m/s²

 

[Alexanddros81]

I got it!

We just assume that a_t just before A is 4.2m/s² and just after A is 4.2m/s²

and then find a_n = 5.55 m/s². Then a = 6.96 m/s²
or

we could do the following:

Is this correct?

 

[Alexanddros81]

Can you check this?