How to find angle from angular velocity?

[haruspex]

will it be 1.5 m/s or zero?

Which of those represents "at rest"?

 

[Sneakatone]

zero is at rest

 

[haruspex]

Right. So there is uniform deceleration from 1.5 m/s to 0 over a distance of 3m. How long does that take?

 

[Sneakatone]

2 seconds

 

[haruspex]

2 seconds

No, it would take 2 seconds to cover 3m at a constant speed of 1.5 m/s, but it it slowing down, so will take longer. What kinematic equation do you know involving two speeds, distance and time when acceleration is constant? If you don't know any such, what kinematic equations do you know?

 

[Sneakatone]

x=vt+1/2at^2

 

[haruspex]

x=vt+1/2at^2

That one involves distance, initial speed, time and acceleration. At this stage, you don't know the acceleration, but you do know the final speed, so you're looking for a different equation. What others do you know?

 

[Sneakatone]

vf^2=vi^2+2add=[(vi+vf)/2]*t

 

[haruspex]

Good, so which of those involves three quantities that you know and the quantity you're trying to calculate?

 

[Sneakatone]

the 1st equation , rearranging it making
a=(vf^2-vi^2)/2d

 

[haruspex]

the 1st equation , rearranging it making
a=(vf^2-vi^2)/2d

We're trying to calculate the time, not the acceleration.

 

[Sneakatone]

so t=d/[(vi+vf)/2]

 

[haruspex]

Right. So using that, how long will it take to come to rest?