Speed and Velocity Formula, Definition, Solved Examples

While velocity takes into account both the speed and direction of an object's motion, speed only considers how quickly an object is moving. When an object moves linearly (in a straight line), both its speed and velocity can be the same. The speed and velocity, however, will vary if the motion involves a change in direction because velocity is a vector.

Distance and Displacement

Displacement and distance are two words used to express how much an object moves in two separate ways. Despite their apparent similarity, physics gives them separate meanings:

Distance

• Distance is a scalar quantity that describes the entire path that an object travels while in motion.
• It counts the distance travelled by an object without taking direction into account.
• Distance is always either zero or positive.
• Taking the aforementioned example, if you were to walk 3 kilometres to the north and then 4 kilometres to the east, you would have covered a total distance of 7 kilometres.

Displacement

• The change in an object's location between its initial point and its final point is referred to as displacement, which is a vector quantity.
• It considers both the magnitude (the distance the object has travelled from the starting point) and the direction of the movement.
• Depending on the direction of the motion, displacement might be positive, negative, or zero.
• The displacement would be the straight line distance from your starting position to your finishing location, which is 5 kilometres at an angle of 53.13 degrees to the north-east, for instance, if you walked 3 kilometres to the north and then 4 kilometres to the east.

Also Check - Centre Of Mass Formula

Speed

Speed is a scalar quantity that represents the rate of movement of an object. The rate at which an item travels a specific distance in a specific length of time is a fundamental idea in physics. Speed, as contrast to velocity, solely considers the amplitude of the motion and ignores the direction of the motion.

Formula of Speed:

S=D/T

Where,

S= speed

D= distance

T= time

Unit of Speed

The measurement system being utilised determines the speed unit. The unit of speed in the International System of Units (SI), which is frequently utilised in scientific and daily situations, is metres per second (m/s). This measurement is the trip in metres divided by the time in seconds.

Average Speed

Average speed refers to the average speed at which an object covers a certain distance. It is determined by dividing the total distance travelled by the total amount of time needed to complete that distance.

Formula for Average Speed

Average Speed =Total Distance/Total Time

Where,

Average Speed: The average rate of motion over a specific distance.

Total Distance: The sum of all the distances covered by the objects.

Total Time: The sum of all the time intervals taken to cover those distances

Also Check - Electrical Resistance Formula

Velocity

A fundamental idea in physics called velocity explains the speed and direction of an object's motion. It has both a magnitude and a direction because it is a vector quantity. Compared to just speed, velocity gives a more comprehensive picture of how an object is moving.

Formula for Velocity: Velocity (v) is calculated by dividing the displacement (change in position) by the time taken:

v =Δ x/Δ t

Where,

v= velosity

Δx= displacement

Δt= time taken

Unit of Velocity

Units used to express velocity include feet per second (ft/s), metres per second (m/s), kilometres per hour (km/h), etc. The unit of distance and the unit of time are combined to form the unit of velocity.

Average Velocity

Average velocity refers to the speed at which an object moves on average during a certain period of time and in a given direction. It considers the object's overall displacement throughout that span of time. Average velocity is calculated using the following formula:

Formula for Average Velocity

average velocity=total distance/total time

In mathematical terms, this can be expressed as:

average velocity=Δx/Δt

Where,

Average Velocity is the average velocity of the object.

Δx= represents the total displacement (change in position) of the object during the time interval.

Δt= is the total time taken for the motion to occur.

Also Check - Wind Energy Formula

Instantaneous Velocity

The term "instantaneous velocity" describes the speed of an object at a certain moment in time. It is the speed at which the displacement of an object in relation to time is changing at that precise moment. Instantaneous velocity is the derivative of the object's displacement function relative to time, according to mathematics.

Formula for Instantaneous velocity

instantaneous velocity= dx/ dt

Where,

Instantaneous Velocity is the velocity of the object at a specific instant in time.

dx represents an infinitesimally small change in displacement at that instant.

dt represents an infinitesimally small change in time at that instant.

dx/ dt represents the derivative of displacement with respect to time.

In practical terms, finding the instantaneous velocity it involves calculus, specifically differentiation. If you have the equation which describes the object's position as a function of time

x(t), you can differentiate this function with respect to time to get the instantaneous velocity function

v(t)= dx/ dt

Alternatively, if you have data points for the position of an object over time, you can calculate the average velocity over decreasingly smaller time periods until it approaches zero, which will give you a rough idea of the instantaneous velocity. This idea is closely related to the calculus idea of a derivative.

Velocity and Acceleration

The rate at which velocity changes in relation to time is known as acceleration. A moving object's velocity alters as it undergoes acceleration. The object moves faster if the acceleration is in the same direction as its initial velocity. The object's speed reduces until it stops and changes direction if the acceleration is in the other direction.

Understanding velocity is essential for comprehending a variety of physical phenomena, from the motion of common objects to more intricate ideas in disciplines like mechanics, fluid dynamics, and astronomy. It is crucial for forecasting and analysing an object's behaviour since it gives insight into the dynamics of objects in motion.

How Speed is Different to Velocity

Although speed and velocity are similar ideas, they each have specific physical definitions. The main distinctions between speed and velocity are listed below:

Vector vs. Scalar:

Speed: Since speed lacks a distinct direction and merely has a magnitude (numerical value), it is a scalar quantity.

Velocity: Because it has both magnitude (a numerical value) and direction, velocity is a vector quantity. It illustrates the direction and speed of an object's motion.

Representation:

Speed: A single numerical value (such as 50 km/h) is used to describe speed.

Velocity: Itis shown as a number value and a direction, such as 50 km/h north.

Directional Consideration:

Speed: The direction of motion is not taken into account by speed. It simply concentrates on the rate at which something is moving.

Velocity: Velocity takes into account both the direction and the speed of motion. The velocities of two objects moving at the same speed but in opposing directions will differ.

Calculation:

Speed: By dividing the distance travelled by the time required, speed is determined. You must consider the ratio of the distances and times because it is a scalar quantity.

Velocity: Calculating velocity involves dividing displacement (change in location) by the amount of time required. Because displacement has both a magnitude and a direction, velocity takes both into account when calculating its value.