Question

A cyclist moving on a circular track of radius \[40m\] completes half a revolution in \[40\sec \]. Its average velocity is:
A) $Zero$
B) \[2m{s^{ - 1}}\]
C) \[4\pi m{s^{ - 1}}\]
D) \[8\pi m{s^{ - 1}}\]

Answer 1

Hint: The unit to measure the total displacement travelled in a certain time period is called velocity. It has both magnitude and direction. Hence the velocity can be either negative or positive. The average is the change of displacement per time ratio. The average velocity changes with respect to time.

Formula used:
\[V = \dfrac{d}{t}\]
Where,
V=velocity,
d=distance covered,
t=time taken to cover the distance.

Complete step by step answer:
Velocity is the rate of displacement travelled. The average velocity is the displacement travelled in a unit time. It has both magnitude and direction. Hence it is called a vector quantity.
The cyclist travelled in a circular track. The circular track displacement is \[2R\]. And the time taken to cover this \[2R\] distance is\[40\sec \].
Hence the average velocity can be find the formula,
\[V = \dfrac{d}{t}\]
Applying the values in the formula,
\[ \Rightarrow V = \dfrac{{2R}}{{40\sec }}\]
\[ \Rightarrow V = \dfrac{{2 \times 40m}}{{40\sec }}\]
On cancelling the terms, we get
\[\therefore V = 2m{s^{ - 1}}\]
Hence the average velocity is \[2m{s^{ - 1}}\].

Hence the correct option is B.

Additional information:
(i) Speed is the rate of distance travelled or the distance travelled in a unit time. Even though the velocity and speed sound the same, speed has only magnitude. Speed doesn’t say about the direction of the moving particle. Hence it is called a scalar quantity.
(ii) The difference between the speed and velocity is that velocity is a vector quantity whereas the speed is a scalar quantity. The velocity can be greater than the value of speed whereas it doesn’t include the direction the particle takes. Hence, we can also say that the displacement can never be greater than the distance.

Note: The velocity is the quantity that describes the direction and the magnitude of speed of any moving object. It can be found when the distance travelled and the time taken to travel that distance. The SI unit of velocity is $m{s^{ - 1}}$. And the dimension of velocity is $L{T^{ - 1}}$.