# Differences between Acceleration and Velocity

Before learning about acceleration and velocity, one needs to understand the concept of motion. Also, one should study other related basic topics such as scalar quantities, vector quantities, and expressing units, etc.

## Motion of an object

When a body or an object is in movement from a fixed point (its position as well) because of the influence from external sources, the body is considered to have undergone a motion. Motion is also known to be displacement.

## Types of motion

Motion is commonly classified into four different types. They are,

• Rotary motion
• Linear motion
• Reciprocatory motion
• Oscillatory motion

They all possess different notions of motion in relation to time even though the variation is very little. For instance, to describe rotational motion, the displacement is said to be angular displacement and similarly for velocity; we have angular velocity and so on.

## Scalar quantities

A scalar quantity is nothing but the measurement of a quantity that is found to be one-dimensional. In simple words, scalar quantity consists of only magnitude. For instance, work, mass, temperature, etc.

## Vector quantities

Vector quantity is defined as the measurement of a quantity that possesses two-dimensional characteristics which means it contains both magnitude and direction. For instance, velocity, acceleration, displacement, etc.

## Units

A unit can be seen as one form of measurement and it is the definite magnitude of a quantity. The following are the 7 physical quantities along with their basic units one should keep in mind:

• Length – meter (m)
• Time – second (s)
• Mass - kilogram (kg)
• Temperature – kelvin (K)
• Electric current – ampere (A)
• Amount of substance – mole (mol)
• Luminous intensity – candela (cd)

These are all described based on their SI units. Apart from that, there is a collection of 7 basic units as well and they are termed as derived quantities. They are derived from fundamental quantities.

For instance, we know that the unit of force is m/s2 or m s-2 or N (which is the abbreviation of Newton). Here, meter can be abbreviated as ‘m’ which came from the physical quantity called length. Meanwhile, ‘s’ is nothing but the abbreviation for second, which is considered as a physical quantity for time. Like this, take another example of fundamental quantity, kg/m3 or kg m-3. Here, ‘kg’ is the representation for kilogram of the physical quantity mass whereas ‘m’ is the abbreviation for meter, whose physical quantity is length.

## Displacement

Displacement of a body is described as the vector difference between the initial point and the end-point of that displaced object. For instance, consider a body which is moving from its initial position (which is its rest position), O. It is forced to travel x distance and made to stop at a new point, P. The distance which is obtained (between the starting point O and the end-point P) can be measured as x. Hence, this change of position of an object is called displacement. Displacement does not necessarily have to be the distance traveled. It can be expressed as given below,

Displacement d = P – O = x m

Where, m is meter, the unit of length.

## Velocity

Velocity can be simply obtained as the rate of change of displacement. When a body is found to be moving in a specified direction along with some specified time, it is considered as velocity. In other terms, when a quantity is capable of specifying both distance and time, it is called velocity. Velocity can be altered by changing the speed or direction or both of them. Velocity can be expressed as follows, This can be further said as,

V=x/t

Where, x is the displacement and t is the time taken. It can be calculated as,

x=end point-starting point

x=v-u

Velocity is a vector quantity. So, it depends on both magnitude and direction. For instance, imagine a truck is traveling at a speed of 30 m/s towards the south in 3 minutes. This describes how quick the truck has moved and in what direction and time taken.

## Acceleration

Acceleration can be defined as the rate of change of velocity. As discussed before, velocity is considered as speed with direction and when the velocity experiences a change consecutively, acceleration is created. For instance, a tennis ball is dropped into a pot of water. The initial speed of the ball is zero, but it gains more and more pace when it reaches near the water, because of gravitational force. So, because of this, the water splashes up when the tennis ball hits it.

Acceleration can be expressed as, where velocity changed from u to v in time t is given above. As acceleration contains both magnitude and direction, it is a vector quantity and its SI unit is m/s2.

Students can refer to NCERT Class 9 Chapter 8 Motion for detailed explanations with examples to understand acceleration and velocity in a better way.

## Comparison table

Comparison Basis Velocity Acceleration
Meaning Speed of an object in a particular direction Change in velocity with respect to time
Calculated With Displacement Velocity
Nature of quantity Vector quantity Vector quantity
Simple definition Rate of change of displacement Rate of change of velocity
Formula Displacement/Time (d/t) Velocity/Time (v/t)
SI unit meter/second (m/s) meter/second2 (m/s2)
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