A particle is moving along a circle with a uniform speed `10 m//s`. At `t = 0` , the particle is moving along east. Find the change in velocity (magnitude and direction) in (a) `1//4th` revolution , (b) `1//2` revolution , ( c) `3//4th` revolution and (d) `1` revolution.

Explanation

(a) Change in velocity `Delta vec(v) = vec(v_(2)) - vec(v_(1)) = vec(v_(2)) + (-vec(v_(1)))`
Here , we want to subtract `vec(v_(1))` from `vec(v_(2))`. For this , reverse the direction of `vec(v_(1))` and then add to `vec(v_(2))`.
`Delta v = sqrt((10)^(2) + (10)^(2)) = 10 sqrt(2) m//s`
`tan theta = (10)/(10) = 1 rArr theta = 45^(@)`
Change in velocity is `10 sqrt(2) m//s` along the north - west.
(b) `Delta v = 10 + 10 = 20 m//s`
Change in velocity is `20 m//s` along the west.
(c ) ` Delta v = 10 sqrt(2) m//s`
`theta = 45^(@)`
Change in velocity is `10 sqrt(2) m//s` along the south - west.
(d) Change in velocity ` = 0`