Question

10. An old person moves on a semi-circular track of radius 40.0 m during a morning walk. If he starts at one end of the track and reaches at the other end, find the distance covered and the displacement of the person.

Answer 1

Hey there !

Thanks for the Question !

Solution:

Given that the track is semicircular. Also the measure of Radius is 40 m.

Key Concepts to be known:

Distance: The Total Length traveled by the body in a particular time. Distance can never be zero or negative and it is always positive. Distance is always greater than or equal to Displacement.

Displacement: The shortest distance between the initial and final points. It can negative, positive and zero also. It is always less than or equal to the distance traveled.

Now let us look into the sum :

So, Distance Traveled = Circumference of the Semicircle

Circumference of a Semi Circle = πr ( 'r' represents the radius )

So Circumference = 3.14 * 40

=> Circumference = 125.6 m

Hence the distance traveled = 125.6 m

Now displacement between the two points is a straight line between the initial and final position. So a straight line would represent the diameter of the semicircle. Hence,

Displacement = Diameter of the semicircle.

=> Displacement = 2r

=> Displacement = 2 * 40 = 80 m

Hence the Distance is 125.6 m and the Displacement is 80 m.

Hope my answer helped !