Velocity Formula

Velocity Formula

Velocity is a vector quantity that describes the rate of change of an object's position with respect to time. It includes both the object's speed and the direction of its motion. While speed only tells us how fast an object is moving, velocity adds the crucial element of direction. For example, a car traveling at 60 mph east has a different velocity than a car traveling at 60 mph west. Learn more about velocity and its formula in this article prepared by Extramarks.

What is Velocity?

Velocity is a fundamental concept in physics that describes the rate of change of an object's position with respect to time. It is a vector quantity, meaning it has both magnitude (numerical value) and direction. In simpler terms, velocity tells us how fast an object is moving and in which direction it is moving.

Velocity is a vector quantity because it includes both magnitude (speed) and direction. It is represented graphically as an arrow, where the length of the arrow represents the speed, and the direction of the arrow represents the direction of motion.

Units of Velocity

The SI unit for velocity is meters per second (m/s). However, it can also be expressed in other units depending on the context, such as kilometers per hour (km/h) or miles per hour (mph).

Velocity Formula

Velocity is a change in an object's displacement over time, as was previously discussed. Simply put, velocity is a measurement of the amount of time it takes an object to move in a particular direction. Additionally, it has an inverse relationship with time travelled and a direct relationship with displacement. Its measurement is in metres per second (m/s).

Velocity = Displacement ÷ time

• Displacement = final position – initial position or change in position
• Time is the time taken to cover the distance.

Now let’s take some values to understand the formula clearly. Suppose Mr. X's initial position is x_i and his final position is x_f and he has taken time 't' to cover this distance, then the equation will be.

v = x_f – x_i / t = Δx / t

Here

• v = velocity,
• x_f = final position of X
• x_i = initial position of X
• t = time taken by the object to move along the distance (s)

Solved Examples on Velocity Formula

Example 1: Suppose there is an object travelling a distance of 10 meters in the left direction and the time taken by the object is 2 minutes. Find the velocity of the object.

Solution:

Now recall the formula, which is velocity = displacement ÷ time

v = d / t

Now put the values in the formula. But first of all change minutes into time by multiplying minutes by 60.

Time in seconds = time in minutes × number of seconds in a minute

t = 2 × 60 = 120 s

So, time in seconds is 120 s

v = 10 / 120

v = 0.08 m/s

The velocity of the object is 0.08 m/s.

Example 2: A car travels from City A to City B, a distance of 300 kilometers, in 5 hours. Determine the velocity of the car.

Solution:

Given:

• Distance traveled, $\Delta x = 300$ kilometers
• Time taken, $\Delta t = 5$ hours

The formula for velocity is: $v = \frac{\Delta x}{\Delta t}$

v = 300km/5h​

$v = 60 \, \text{km/h}$

The velocity of the car traveling from City A to City B is $60\text{km/h}$.

Example 3: A runner completes one lap around a circular track with a circumference of 400 meters in 2 minutes. Determine the velocity of the runner.

Solution:

Given:

• Circumference of the track, x = 400 meters
• Time taken to complete one lap, $\Delta t=2$ minutes

Solution: The formula for velocity is: v = Δx/Δt​

Convert time from minutes to hours: Since velocity is typically measured in meters per second or meters per hour, we need to convert the time from minutes to hours:

Substitute the given values: v = 400 m/(1/30)​

Calculate: $v = \frac{400 \, \text{m}}{\frac{1}{30} \, \text{h}} = 400 \times 30 = 12000 \, \text{m/h}$

The velocity of the runner completing one lap around the track is $12000 \, \text{m/h}$.