Velocity and Acceleration Science Notes Class 8

Following is the velocity and acceleration notes for grade 8 students. Velocity and Acceleration are derived physical quantities as they depend upon fundamental physical quantities directly. In this chapter, we will discuss velocity, average velocity, relative velocity, acceleration and retardation.

Velocity

Definition I: Velocity is the rate of change of displacement.

Definition II: Velocity is defined as the ratio of change of displacement to time taken.

Displacement is defined as the shortest distance between any two fixed points. Or, the distance traveled by a body in a straight line is called displacement.

Mathematically,

$\text{Velocity (v)} = \displaylines{ \text{displacement (s)} \\ \overline{\text{time taken (t)}} }$

Important terms:

Initial velocity: The velocity of a body measured at the beginning of the journey is called initial velocity. It is represented by ‘u’.
Final velocity: The velocity of a body measured at the end of the journey is called final velocity. It is denoted by ‘v’.
Uniform velocity: If a body covers equal displacement in equal interval of time, it is said to have uniform velocity. Example: velocity of light.
Non-uniform velocity: If a body covers unequal displacement in equal interval of time or equal displacement in unequal interval of time, it is said to have non-uniform velocity. Example: velocity of a running boy.

Average Velocity

Let us suppose a car A travels a journey of 10km in a straight road in 15 minutes. Say, he kept on increasing and decreasing the car’s speed from 40 kmph to 60 kmph. Since he was travelling in a straight road, it can be regarded as velocity. From the condition given, it can be noted that the velocity was not constant during the whole journey. But, there is definitely an average velocity that would represent his entire journey which can be obtained as total displacement covered divided by total time taken for the ride.

Owing to above conditions, average velocity of any body is defined as the mean velocity with which the object covered the entire displacement in the given time.

In general, average velocity of a body is defined as the ratio of total displacement covered to time taken.

Mathematically,

$\text{Average velocity (v}_\text{av)} = \dfrac{ \text{total displacement (s)}}{ \text{total time taken (t)}}$

Also,

$\text{Average velocity (v}_\text{av)} = \dfrac{ \text{initial velocity (u) + final velocity (v)} }{\text{2} }$

$\text{v}_\text{av} = \displaylines{\text{ u + v} \\ \overline{2}}$

Thus, average velocity can also be defined as the arithmetic mean of initial and final velocity of a body.

Relative Velocity

Relative velocity is a measure of velocity of one body with respect to another body. The another body is also called as reference point.

Reference point is the point with respect to which the velocity of a given body is measured. Reference point can be another moving body or a stationary body.

If two bodies A and B are moving towards the same direction, then

the relative velocity of A with respect to B is given by (velocity of A – velocity of B).
the relative velocity of B with respect to A is given by (velocity of B – velocity of A).

If two bodies A and B are moving in opposite direction, then

the relative velocity of A with respect to B is given by (velocity of A + velocity of B).
the relative velocity of B with respect to A is given by (velocity of B + velocity of A).

Acceleration and Retardation

Acceleration and retardation are two opposite terms. Retardation is also called as negative acceleration.

In physics, when a body increases its velocity over time, we say the body is being accelerated. And, whenever the body decreases its velocity over time, we say the body is retarding.

Thus, in general understanding, acceleration is the positive change in velocity of a body and retardation is the negative change in velocity of a body.

Acceleration causes body to move in forward direction while retardation causes body to move in backward direction.

Acceleration

Acceleration is defined as the positive rate of change of velocity of a body. It is denoted by ‘a’.

Mathematically,

$\text{acceleration (a)} = \dfrac{ \text{final velocity (v) – initial velocity (u)} }{ \text{time taken (t)}}$

Retardation

Retardation is defined as the negative rate of change of velocity of a body. It is denoted by ‘-a’.