A body is moving with uniform speed v on a horizontal circle in anticlockwise direction from A as shown in figure. What is the change in velocity in (a) half revolution (b) first quarter revolution.

Explanation

Change in velocity means `DeltavecV = vecV_(f) - vecV_(i)`
(a) As show an in fig.3.25 (b) , for the half revolution
`if " "vecV_(3)= vecV" and vecV_(1)= - vecV`
`So, " " DeltavecV= vecV_(3) - vecV_(1) = vecV- (-vecV)`

`i.e., " "DeltavecV = 2vecV`
`i.e., " "DeltavecV = 2v "directed south"`
(b) As show in fig.3.25 (c),for quarter revolution :
`" "DeltavecV= vecV_(2)- vecV_(1) and theta= 90^(@)`
`So," "DeltaV= sqrt(v^(2) +v^(2))= (sqrt(2))v`
`and " "phi= tan^(-1)((v)/(v))= 45^(@)`
`therefore" " DeltavecV=(sqrt(2))v "south-west"`