Speed Velocity and Acceleration Formulas, Definition, Examples [physics]

Physics is the study of nature and its laws. We expect that all these different events in nature take place according to some basic laws and revealing these laws of nature from the observed events in physics. Here we are going to discuss an important topic related to physics in accessible words. Curious to learn? Then you are on the right platform.

After understanding and analyzing Speed, Velocity, and Acceleration the most important and useful conclusions are:

SPEED = DISTANCE / TIME [it is a scalar quantity, its SI unit is meter per second (m/s)]
VELOCITY = DISPLACEMENT / TIME [it is a vector quantity, its SI unit is meter per second (m/s)]
ACCELERATION = CHANGE IN VELOCITY/ TIME [it is a vector quantity, its SI unit is meter per second square (m/s2)

What we have on this table

• Speed / Definition and Formula / Four types of Speed
• Velocity / Definition and Formula / Five types of Velocity
• Acceleration / Definition and Formula / Two types of Acceleration
• So let’s get to know about SPEED, VELOCITY, and ACCELERATION in more detail.

What is SPEED

Speed is a physical measurement quantity that measures how far an object has traveled in a given amount of time. For example, if a car covers a distance of 10 km in 1 hour then the speed of the car is 10km/hour and 2.778 meters per second. SI unit of speed is meter per second abbreviated as m/s. The dimension of speed is LT-1 (here, L = length, T = time). Speed is a scalar quantity so it has only magnitude, not direction.

SPEED definition

SPEED is defined as the distance traveled by the moving object in the unit time interval.

Speed meaning

The meaning of speed is described as changing the physical location rapidly of any object. If an object is rapidly changing its location and time then the object is in a process of speed.

Important speed formula

The formula of speed is DISTANCE / TIME

[ s = d/t, where S is speed, d is the distance traveled and t is the time taken]

Further elaborating the formula of speed, it is calculated on the basis of distance and time. The formula for the speed is defined as the distance traveled by the particle divided by the time interval.

An important example of Speed

Suppose a moving object traveled a distance of 5 kilometers and it took 1 hour to cover that distance, then the speed of the object is 5 kilometers per hour. Converting in Standard International unit, there is 5000 meter in 5 meters and 60 seconds in 1 hour. So when we divide 5000 meters by 60 seconds we got the object's speed In terms of SI units i.e. 1.389 meters per second.

Types of Speed

There are four types of speed in physics

• Uniform speed
• Non-uniform speed/Variable speed
• Average speed
• Instantaneous speed

What is the uniform speed?

When an object is covering a specific distance in every specific interval of time then the speed is said to be Uniform. For example, if a car covering a distance of 10 kilometers in 1 hour and again it covers the next 10 kilometers in 1 hour and so on, then the car is in uniform speed.

The formula for uniform speed

As the distance and time remains the same in uniform speed so the formula for uniform speed is that the basic formula of speed i.e. speed = distance/time

What is Non-uniform speed?

When the distance covered by an object continuously changes in every specific interval of time, then the speed is said to be non-uniform or variable. For example, if an object covers a distance of 10 kilometers in the first hour, 9 kilometers in the second hour, 15 kilometers in the third hour, and so on, then the speed is said to be variable speed.

What is Average speed?

The average speed of any object is defined as the total distance covered by the object in total intervals of time. For example, suppose an object covers a distance of 10 km in 1st hour, 15 km in the 2nd hour and, 20 km in the 3rd hour, then the average speed is calculated by dividing the total distance (10km+15km+20km) by total time taken(1 hour+1hour+1hour). So the average speed is 45km/3hours = 15 kilometers per hour. In terms of SI unit, it is 4.167 meters per second.

The formula for average speed

Average speed = total distance/total time

If the particle travels a distance s in time t1 to t2, the average speed is defined as vav = s/t2 − t1

Explanation of average speed:

The average speed of a particle in a time interval is defined as the distance traveled by the particle divided by the time interval. The average speed gives the overall “rapidity” with which the particle moves in this interval.

An important question related to average speed:

Question: The distance traveled by an object in time t is given by s = (2. 5 m/s2) t2. Find the average speed of the particle during the time 0 to 5 seconds.

Answer: The distance travelled during time 0 to 5 seconds is

s = (2. 5 m/s2 )(5s)2 = 62.5 m

The average speed during this time is vav = 62.5 m/ 5 s = 12.5 m/s

What is Instantaneous speed?

Instantaneous speed is defined as the sudden change in the speed of any object in a particular moment of time. For example, an object is moving at a speed of 2 m/s then it suddenly increases its speed to 4 m/s and then after 10 seconds it again increases its speed up to 6 m/s and after the next 5 seconds, it drops its speed to 3 m/s. here the speeds of 4 m/s, 6 m/s, and 3 m/s are instantaneous speeds.

What is the formula of instantaneous speed?

The formula for instantaneous speed is [v = ds/dt, where v is instantaneous speed, ds is the distance covered during instantaneous speed, dt is the time interval at that particular instantaneous speed]

Explanation of Instantaneous Speed

A man starts running, he runs slowly and gradually increases his speed. We define the instantaneous speed at a time t as follows:

Let Δs be the distance traveled in the time interval t to t + Δt. The average speed in this time interval is vav = Δs/Δt

Now make Δt negligibly small and look for the value of Δs/Δt

Remember Δs is the distance traveled in the chosen time interval Δt.

As Δt approaches 0, the distance Δs also approaches 0 but the ratio Δs/Δt has a finite limit.

The instantaneous speed at a time t is defined as v = limΔt → 0 Δs/Δt = ds/dt

Where s is the distance traveled in time t. The average speed is defined for a time interval and the instantaneous speed is defined at a particular instant.

What is velocity?

Velocity is a physical measurement quantity that measures how much an object is displaced in a given amount of time. It is a vector quantity. For example, if an object moves from its initial position by 10 meters in a particular direction and the time taken by the object during this is 1 second, then the velocity of the object is 10 meters per second. SI unit of velocity is Meter per second abbreviated as m/s. It is a vector quantity so it has both magnitude and direction.

Velocity definition

The velocity of a moving particle is defined as the displacement of the particle in a unit time interval.

Velocity meaning

The meaning of Velocity is described as changing the physical location of any object in a particular direction. If an object is changing its location along with time in a particular direction then the object is in a process of velocity.

The important formula of velocity

The formula of speed is DISPLACEMENT / TIME

[ V = Δx/Δt, where v is velocity, Δx is the displacement and Δ t is the time taken]

Further elaborating the formula of velocity, it is calculated on the basis of displacement and time. The formula for the velocity is defined as the displacement covered by the particle divided by the time interval.

An important example of Velocity

Suppose a moving object moves a distance of 5 kilometers in a particular direction in 1 hour, then the velocity of the object is 5 kilometers per hour. Converting in Standard International unit, there is 5000 meter in 5 meters and 60 seconds in 1 hour. So when we divide 5000 meters by 60 seconds we got the object's velocity In terms of SI units i.e. 1.389 meters per second.

Types of velocity

There are five types of velocity in physics

• Uniform velocity
• Non-uniform velocity/Variable velocity
• Average velocity
• Instantaneous velocity
• Angular velocity

What is the uniform velocity?

When an object is covering a specific distance in every specific interval of time in a particular direction then the velocity is said to be Uniform. For example, if a car in a particular direction covering a distance of 10 kilometers in 1 hour and again it covers the next 10 kilometers in 1 hour and so on, then the car is in uniform velocity.

The formula for uniform velocity

As the displacement and time remains the same in uniform velocity so the formula for uniform velocity is that the basic formula of speed i.e. velocity = displacement/time

What is Non-uniform velocity?

When the displacement covered by an object continuously changes in every specific interval of time, then the velocity is said to be non-uniform or variable. For example, if an object in a particular direction displaced by a distance of 10 kilometers in the first hour, 9 kilometers in the second hour, 15 kilometers in the third hour, and so on, then the velocity is said to be variable velocity.

What is Average velocity?

The average velocity of any object is defined as the total displacement covered by the object in total intervals of time. For example, suppose an object in a particular direction covers a distance of 10 km in 1st hour, 15 km in the 2nd hour and, 20 km in the 3rd hour, then the average velocity is calculated by dividing the total displacement (10km+15km+20km) by total time taken(1 hour+1hour+1hour). So the average velocity is 45km/3hours = 15 kilometers per hour. In terms of SI unit, it is 4.167 meters per second.

The formula for average velocity

Average velocity = total distance/total time

If the particle moves by a displacement x in time t1 to t2, the average velocity is defined as vav = x/t2 − t1

Explanation of average velocity

The average velocity of a particle in a time interval is defined as the displacement covered by the particle divided by the time interval. The average velocity of a particle in a time interval t1 to t2 is defined as its displacement divided by the time interval.

If the particle is at a point A at time t = t1 and at B at time t = t2, the displacement in this time interval is the vector AB ®

The average velocity in this time interval is then, v ® av = AB ®/ t2 - t1

An important question related to average speed:

Question: A table clock has its minute hand 4 cm long. Find the average velocity of the tip of the minute hand between 6.00 a.m. to 6.30 a.m.

Answer: At 6. 00 a.m. the tip of the minute hand is at 12 mark and at 6. 30 a.m. or 6. 30 p.m. it is 180° away. Thus, the straight line distance between the initial and final position of the tip is equal to the diameter of the clock. Displacement = 2 R = 2 × 4 cm = 8 cm.

The displacement is from the 12 mark to the 6 mark on the clock panel. This is also the direction of the average velocity.

The time taken from 6.00 a.m. to 6.30 a.m. is 30 minutes = 1800 s.

The average velocity is vav = Displacement/time = 8 cm/1800 s = 4. 4 × 10−3 cm/s.

What is Instantaneous velocity?

Instantaneous velocity is defined as the sudden change in the velocity of any object in a particular moment of time. For example, an object is moving in a particular direction with a velocity of 2 m/s then it suddenly increases its velocity to 4 m/s, and then after 10 seconds it again increases its velocity up to 6 m/s and after the next 5 seconds, it drops its velocity to 3 m/s. here the velocities of 4 m/s, 6 m/s, and 3 m/s are instantaneous velocities.

What is the formula of instantaneous velocity?

The formula for instantaneous velocity is [v → av = ∆r/∆t, where v → av is instantaneous velocity, ∆r is the displacement covered during instantaneous velocity, ∆t is the time interval at that particular instantaneous velocity]

Angular velocity

The angle subtended by the line joining the object from the origin of the circle in a unit time interval is called angular velocity.

Angular velocity formula/equation

angular velocity is generally denoted by ω and ω = ϴ/t, where ϴ is the subtended angle, t = time interval

If T = time taken by the object to complete one revolution

Η = frequency = no. of revolutions in one second.

Then ηT =1 and ω = 2π/T = 2πη.

Note: in one revolution, the object travels 2πr distance.

Therefore, Linear speed = 2πr/T = ωr = angular speed * radius

What is Acceleration?

Acceleration of an object is defined as the rate of change of velocity of the object. It is a vector quantity and its SI unit is meter per second square abbreviated as m/s2. if velocity decreases with time then acceleration is negative and is called Retardation.

Formula of Acceleration

The formula for acceleration is defined by the change in velocity per unit time i.e. Acceleration = Change in velocity/time

ā=Δv/Δt where ā is acceleration, Δv is change is velocity and, Δt is the time interval.

Types of acceleration

There are two types of acceleration

• Average acceleration
• Instantaneous acceleration

Explanation of Acceleration

If the velocity of a particle remains constant as time passes, we say that it is moving with uniform velocity. If the velocity changes with time, it is said to be accelerated. The acceleration is the rate of change of velocity. Velocity is a vector quantity hence a change in its magnitude or direction or both will change the velocity.

Suppose the velocity of a particle at time t1 is v 1 and at time t2 it is v2. The change produced in time interval t1 to t2 is v2 − v1. We define the average acceleration a av as the change in velocity divided by the time interval. Thus, aav = v2 − v1 / t2 − t1

Again the average acceleration depends only on the velocities at time t1 and t . How the velocity changed in between t1 and t2 is not important in defining the average acceleration. Instantaneous acceleration of a particle at time t is defined as a= lim ∆t → 0 ∆v/ ∆t = dv/ dt

Where ∆v is the change in velocity between the time t and t + ∆t. At time t the velocity is v and at time t + ∆t it becomes v+ ∆v . ∆v / ∆t is the average acceleration of the particle in the interval ∆t. As ∆t approaches zero, this average acceleration becomes the instantaneous acceleration.