A particle is moving along a circle of radius `R` with a uniform speed `v`. At `t = 0` , the particle is moving along the east. Find the average acceleration (magnitude and direction) in (a) `1//4 th` revolution and (b) `1//2` revolution.

Explanation

(a) `Delta v = sqrt(2) v, NW` (as in the previous problem)
Time period of revolution `T = ( 2pi R)/(v)`
Here , `Delta t = (T)/(4) = ( pi R)/( 2v)`
Average acceleration `bar(a) = (Delta v)/(Delta t) = (sqrt(2) v)/((pi R)/( 2v))`
`= (2 sqrt(2) v^(2))/(pi R),NW`
(b) `Delta v = 2v , W` (as in the previous problem)
`Delta t = (T)/(2) = (pi R)/(v)`
Average acceleration `bar (a) = (Delta v)/(Delta t) = (2v)/((pi R)/(v)) = (2 v^(2))/(pi R) , W`