Constant acceleration and radius of curvature

[Jahnavi]

Homework Statement

Homework Equations

The Attempt at a Solution

The normal acceleration of the particle at any instant is given by a_n = v²/r . v is the speed at any time and r is the radius of curvature . Minimum radius will occur when ratio v²/a_n is minimum .

I think this will occur when the component of velocity along the direction of acceleration becomes zero .

Component of velocity perpendicular to acceleration = 4m/s remains unchanged

At this instant the acceleration vector is perpendicular to the velocity .The net acceleration is the normal acceleration .

And magnitude of normal acceleration = 2m/s² and speed = 4m/s .

Radius = 8m/s

Is it correct ?

 

[haruspex]

The normal acceleration of the particle at any instant is given by a_n=v²/r . v is the speed

No, where v is the tangential speed.
Edit: not sure that's right either.

I think this will occur when the component of velocity along the direction of acceleration becomes zero

Perhaps, but you need a better reason for your answer than a guess.

 

[Jahnavi]

Then , how should I approach this problem ?

 

[haruspex]

Then , how should I approach this problem ?

You could write the equation of motion. Or see if you can justify your guess.

 

[Jahnavi]

Or see if you can justify your guess.

Please help me do that .

 

[haruspex]

Please help me do that .

I cannot think of a way. I would just get going with the equations.

 

[Jahnavi]

Ok