Question

Define velocity. State its unit.

A.)Velocity is defined as the rate of change of distance of the body with respect to time. Its unit in SI is \[{km}/{s}\;\].
B.)Velocity is defined as the rate of change of displacement of the body with respect to time. Its unit in SI is \[{km}/{s}\;\].
C.)Velocity is defined as the rate of change of distance of the body with respect to time. Its unit in SI is \[{m}/{s}\;\].
D.)Velocity is defined as the rate of change of displacement of the body with respect to time. Its unit in SI is \[{m}/{s}\;\].

Answer 1

Hint: Speed is path length by the time taken. Velocity changes in position by the time taken. Then the unit of velocity is \[{m}/{s}\;\].

Complete step by step answer
We are very familiar with the speed. While driving a vehicle, we will compare the speed of your car to others. Or while playing games or solving problems; speed is a significant factor. Speed is related to time.

For example, if a person travels from a point A to another point B. And the time taken for this is supposed to be 10 minutes. Like that, a second person covered the same distance within 9 minutes. Then we will say that the second person is faster than the first. Which means the distance travelled by both of them is the same, whereas the time taken is not is not the same.

So generally speed is defined as the rate of change of distance of body with respect to time. Or

\[Speed=\dfrac{Distance}{Time\text{ }taken}\]

Since distance is a scalar quantity, speed is also scalar. It does not depend on the direction of the motion.

Since in the SI system, the unit of length is the meter and for times it is second. The unit of speed in the SI system is \[{m}/{s}\;\].

Now that it comes to velocity, we cannot merely take as distance travelled by the time taken. Here we should consider the direction of motion too. Then displacement will replace the distance. Displacement is change in position. i.e. final position-initial position.

Then velocity is defined as the rate of change of displacement of the body with respect to time. Displacement is a vector quantity which has both magnitude and direction. So velocity is also a vector quantity. Then the equation to find the velocity is written as

\[Velocity=\dfrac{change\text{ }in\text{ }position}{Time\text{ }taken}\]i.e.
\[Velocity=\dfrac{Displacement}{Time\text{ }taken}\].

In the SI system, the displacement and distance share the same unit.

Therefore the unit of velocity is also \[{m}/{s}\;\].

Thus from the given options D is the answer.

Note: While solving the numerical, please keep in mind that speed is always positive. But velocity can have both positive and negative values. Since displacement is a vector quantity, it depends on the direction of motion.