Motion: Speed, Velocity and Acceleration

Speed: –

Speed of a body is defined as the distance travelled by it per unit time.

i.e hence S.I Unit of speed is metre /sec. (m /s or ms ^{– 1})

Uniform speed:

If a moving body covers equal distances in equal interval of time, then the speed of the body said to be uniform speed

Example:

Suppose a car travels 5 m in every second throughout its Journey then the speed of this car is uniform.

Non- Uniform Speed: –

If a moving body covers unequal distances in equal interval of time, then the speed of the body is said to be non uniform speed.

Example: –

Suppose a car travels 5 m in first second, 10 m in second second, 7 m in third second, 9 m in fourth second, and so on. Then the speed of this car is changing with time and is said to be non- uniform.

Average Speed: –

Average speed of a moving body is defined as the ratio of the total distance travelled by it to the total time taken by it to cover the distance.

Thus V_av

Example: –

When a bus starts its journey from a bus stand, it moves slowly and then its speed is increased Now if it enters a crowded road its speed decreases.

After crossing the crowded road, its speed increases. After traveling few kilometers, suppose the bus has to be stopped, then its speed again decreases. Thus we see that the bus is not moving with the same speed during the whole journey.

Now if we added total distance covered by the bus with different speeds and divide it by the total time taken, then we get the average speed of the bus.

Velocity: –

Velocity of an object is defined as the displacement of the body per unit time

OR,

Velocity of an object is defined as the distance travelled by it per unit time in a particular direction.

i.e.

Hence S.I. unit of velocity is metre /sec (m/s)

Uniform velocity: –

If a moving body covers equal displacement (i.e. equal distance in a particular direction) in equal intervals of time, then the velocity of the body is said to be uniform velocity.

Example: –

Suppose a car travels 5 m in every second in a particular direction then the velocity of car is uniform.

Non- uniform velocity: –

If a moving body makes unequal displacement in equal interval of time, then the velocity of the body is said to be non-uniform velocity.

Example: –

Let a car moves over a horizontal road along the east direction. Let its cover unequal distances in each hour, then the velocity of this car is non uniform.

Average Velocity: –

when the velocity of an object changes with time, then the average velocity is defined as the ratio of the total displacement made by it to the total time taken by it

Note:

If the velocity of an object changes at uniform rate in a particular direction, then the average velocity of the object is equal to the mean of the initial and final velocities of the object.

i.e.

where u = initial velocity of the object

v = final velocity of the object

Note: –

Velocity of a body can be changed in two ways.

(i) By changing the speed of the body while keeping the direction of motion of the body same.

(ii) By changing the direction of motion of the body, but keeping the speed of the body same.

e.g. The velocity of a ball dropped from the top of a building changes, because its speed changes although its direction of motion remains the same.

Also, the velocity of a car, moving in a circular path changes, because its direction of motion changes continuously although it is moving with a constant speed.

Difference between speed and velocity

Speed	Velocity
1. Speed of a body is defined as the distance travelled by it per unit time i.e. 2. Direction is not associated with speed. 3. Speed is a scalar quantity. 4. Speed is always positive. 5. Its value can not be zero for a moving body.	1. Velocity of a body is defined as the displacement of the body per unit time i.e. . 2. Direction is associated with velocity 3. Velocity is a vector quantity 4. Velocity can be positive or negative 5. Its value is zero if initial and final position of the body is same.

Acceleration: –

In non-uniform motion, the velocity of a body changes with time. The change in velocity of an object with time is expressed by a physical quantity known as acceleration.

Acceleration tells us, by how much amount the velocity of a body changes in unit interval of time.

In other words, the acceleration is a quantity which measures how quickly the velocity of a body or an object changes

Acceleration of a body is defined as the change in velocity per unit time

i.e.

acceleration

Acceleration is a vector quantity and its unit is m/s/s or m/s² or ms ^{– 2}

Uniform Acceleration:

If the velocity of an object changes by an equal amount in equal interval of time, then the acceleration of the object is known as uniform acceleration.

e.g. acceleration of freely falling body

Acceleration of a ball rolling down on a smooth inclined plane.

Non- uniform acceleration:

If the velocity of an object changes by an unequal amount in equal interval of time, then the acceleration of the object is known as non-uniform acceleration.

e.g. acceleration of a bus on a crowed road

Uniform circular motion:-

The circular motion of a body having constant or uniform speed is known as uniform circular motion.

How uniform circular motion is an accelerated motion?

When a body moves in a circular path with constant speed, its direction of motion changes continuously.

It means that the body moving in a circular path, changes its velocity. And we know that the change of velocity of a body with time gives rise to an acceleration.

Thus the uniform circular motion is accelerated motion.