Question

A particle is moving in a circle of radius r having centre at O, with a constant speed v. The magnitude of change in velocity in moving from A to B is?

Answer 1

In this question, we will use the relation between the difference of the velocities and its resultant velocity. Further, substituting the given values in the equation will help us to get the required result. Also, we will study the basic difference between speed and velocity, for our better understanding.

Formula used:
$\left| {{{\vec V}_A} - {{\vec V}_B}} \right| = \sqrt {V_A^2 + V_B^2 - 2{V_A}{V_B}\cos \theta }$

Complete answer:
As we know the magnitude of change in velocity of the particle moving from A to B.
$\left| {{{\vec V}_A}} \right| = V\left| {{{\vec V}_B}} \right| = V$
$\Rightarrow \left| {{{\vec V}_A} - {{\vec V}_B}} \right| = \sqrt {V_A^2 + V_B^2 - 2{V_A}{V_B}\cos \theta }$
Now, by substituting the given values in the above equation and further solving, we get:
$\left| {{{\vec V}_A} - {{\vec V}_B}} \right| = \sqrt {V_{}^2 + V_{}^2 - 2{V^2}\cos \theta }$
$\Rightarrow \left| {{{\vec V}_A} - {{\vec V}_B}} \right| = \sqrt {V_{}^2 + V_{}^2 - \dfrac{{2{V^2}}}{2}}$
$\Rightarrow \left| {{{\vec V}_A} - {{\vec V}_B}} \right| = \sqrt {{V^2}}$
$\therefore \left| {{{\vec V}_A} - {{\vec V}_B}} \right| = V$
Therefore, we get the required answer of the magnitude of change in velocity when the particle is moving from A to B.

Additional information:
We already know the basic difference of speed and velocity i.e., speed is the measure of how fast an object can travel, whereas velocity tells us the direction of this speed. Speed is a scalar quantity that means it has only magnitude, whereas velocity is a vector quantity that means it has both magnitude and direction. The S.I unit of velocity is meter per second (m/sec).
A speedometer also called a speed meter is a gauge that measures and displays the instantaneous speed of a vehicle. It is mostly mounted on bikes, cars, scooters. We also know that the speedometer used to measure the speed of a vehicle and the entire vehicle indicate speed in km/h.
The speed of sound is different in different mediums. Further, the speed that is more than the speed of sound is termed differently like- supersonic, hypersonic etc

Note:
This question can be directly answered by knowing the basic concept of speed and velocity. Since, we know speed does not have any direction therefore, speed cannot be negative. We must remember that the unit of speed and velocity is the same i.e., meter per sec or m/s.