1. A circular cycle track has a circumference of 314 m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a velocity of constant magnitude 5.7 m/s. Calculate
a) The distance moved by the cyclist b) the displacement of the cyclist if AB represents north-south direction c) the average velocity of the cyclist
1. A circular cycle track has a circumference of 314 m with AB as one of its diameter. A cyclist travels from A to B along the circular path with a velocity of constant magnitude 5.7 m/s. Calculate
a) The distance moved by the cyclist b) the displacement of the cyclist if AB represents north-south direction c) the average velocity of the cyclist
Let, ‘r’ be the radius of the circular track.
Given,
Circumference, 2πr = 314
=> 2(3.14)r = 314
=> r = 50 m
Therefore, Diameter AB = 2r = 100 m
Speed along the circular path from A to B is 5.7 m/s.
a)
Distance moved by the cyclist is half the circumference, which is 314/2 = 157 m
b)
If AB represents North-South direction then displacement is from A to B which is AB = 100 m and the direction is from north to south.
c)
Time taken to cover half circle is, t = 157/5.7 = 27.54 s
While, the displacement is only, AB = 100 m
So, average velocity is, v = AB/t = 3.6 m/s
Let, ‘r’ be the radius of the circular track.
Given,
Circumference, 2πr = 314
=> 2(3.14)r = 314
=> r = 50 m
Therefore, Diameter AB = 2r = 100 m
Speed along the circular path from A to B is 5.7 m/s.
a)
Distance moved by the cyclist is half the circumference, which is 314/2 = 157 m
b)
If AB represents North-South direction then displacement is from A to B which is AB = 100 m and the direction is from north to south.
c)
Time taken to cover half circle is, t = 157/5.7 = 27.54 s
While, the displacement is only, AB = 100 m
So, average velocity is, v = AB/t = 3.6 m/s
