A particle moves in a circular path of radius 7 cm. It covers (i) half of the circle in 4s and (ii) one complete round in 10 s. In each case find the average speed and average velocity.

Explanation

The circumference of the circle
`= 2pir = 2 xx (22)/(7) xx 7 = 44` cm

(i) The distance travelled by the particle = half of the circumference = `(44)/(2) = 22` cm and time taken = 4 s.
`:.` Average speed v = `(22)/(4) = 5.5 "cm". s^(-1)`.
Displacement = diameter of the circle = `2xx7 = 14` cm and time taken = 4 s.
Hence average velocity, `vecv=(14)/(4) = 3.5 "cm".s^(-1)` along AB.
The distance travelled by the particle = circumference of the circle = 44 cm and time taken = 10s.
`:.` Average speed = `(44)/(10) = 4.4 "cm". s^(-1)`.
Displacement in this case is 0 (as initial and final positions are the same.)
Hence, average velocity = `("displacement")/("time")` = 0.