A car moves on a circular track at constant speed. Take any arbitrary time and c

Question

A car moves on a circular track at constant speed. Take any arbitrary time and call it t0. Suppose that t1 is a later time at which the car has advanced half a circle with respect to its position at t0. What is true regarding the magnitude of the average velocity between t0 and t1? A or B or C or D or E?

A) The magnitude of the average velocity is the same as the speed.
B) The magnitude of the average velocity is a factor of larger than the speed.
C) The magnitude of the average velocity is a factor of smaller than the speed.
D) The magnitude of the average velocity is a factor of /2 larger than the speed.
E) The magnitude of the average velocity is a factor of /2 smaller than the speed.

Explanation / Answer

Velocity = Displacement /time
Speed = Distance /time

Let the Radius of Circle = r
In a Circle When the  car has advanced half a circle,

Total Distance travelled = *r
Total Displacement = 2*r

Time is same in both the cases, therefore
Velocity = 2*r/t
Speed = *r/t

Speed/Velocity = *r/2*r
Speed/Velocity = /2
Speed = /2 * Velocity.
Velocity = Speed / (/2 )

Correct option - (E) The magnitude of the average velocity is a factor of /2 smaller than the speed.

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