a particle moves in a ciorcle of radius 21/22 mwith constant speed 1m/s.find:a)magnitude of av velocityb)magnitude of av acceleration in 2 secs.

Dear Student

Particle will cover a distance of 2m in 2sec.

circumference of circle= 2*22/7*21/22 = 6m

in 6m angular displacement is 360⁰. so in 2m it will be 120⁰

join centre to the initial and final position of the particle. it will be a triangle with 120⁰ angle at the centre and other two angle equal to 30⁰ each.  length of cord will give the displacement.

if rad is R then

displacement= 2Rcos30⁰= 2*21/22*√3 /2 = 21√3/2

avg vel =disp/time= 21√3/4

let at t=0 v1= i (i is unit vector along x axis) and particle is moving clockwise

at t=2 , v2= -sin30⁰ i + -cos30⁰ j= -i/2 - √3 /2 j

v2-v1= -3i/2 - √3 /2 j

avg acc= (-3i/2 - √3 /2 j)/2

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