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17) A particle is moving in a circular path (anti-clock wise direction) of radius 18m. It starts from
point A and completes its journey at B which covers 25% of the circumference of the circular
path in 10s (see the figure 3). Find
a) The distance that the particle travelled
b) The speed of the particle
c) The displacement of the particle
d) The velocity of the particle
a) The distance that the particle traveled can be found by calculating the circumference of the circular path and then multiplying by the fraction of the circumference covered (25%).
Circumference = 2πr = 2π(18m) ≈ 113.097m
Distance traveled = 0.25 * 113.097m = 28.274m
b) The speed of the particle is calculated by dividing the distance traveled by the time taken.
Speed = Distance traveled / Time taken = 28.274m / 10s ≈ 2.8274 m/s
c) The displacement of the particle can be found by calculating the straight line distance between points A and B, which is the diameter of the circle.
Diameter = 2r = 2(18m) = 36m
Displacement = Diameter = 36m
d) The velocity of the particle is a vector quantity and is given by the displacement divided by the time taken.
Velocity = Displacement / Time taken = 36m / 10s = 3.6 m/s (in the direction of motion, which is tangential to the circular path)