A particle moves in a circle of radius `R = 21/22 m` with constant speed `1 m//s.` Find,
(a) magnitude of average velocity and
(b) magnitude of average acceleration in 2 s.

Answer

`0.87`

Explanation

Distance travelled in ` 2 s = AB = 1 xx 2 = 2 m`
`:. theta = (L)/(r) = (AB)/( R) = 2 xx (22)/(21) = (44)/( 21) = (44)/(21)` radian ` = (2)/(3) pi`
Am ` = r sin "" (theta)/( 2) = r sin "" (22)/(11) = r sin "" (pi)/(3)`
`:. AB = 2 xx (21)/(22) sin "" (pi)/(3)`
`= (21)/( 11) xx ( sqrt(3))/( 2) = (21)/( 22) sqrt(3)`
Now for acceleration
Change in velocity ` = | vec (v)_(f) + ( - vec (v)_(i)) |`
` = sqrt( v^(2) + v^(2) + 2 xx v xx v cos "" (pi)/(3))`
`= sqrt( 1 + 1 + 2 xx 1 xx 1 xx (1)/(2)) = sqrt(3)`
`:. a_("avg") = ("Change in velocity ")/("Time")`
`= ( sqrt(3))/( 2) ~~ 0.87 m//s^(2)`