# Measuring The Rate Of Change Of Motion

Quantification of the rate of change of motion of an object is used in every sphere of life. Be it defining the speed limit for the vehicles in an area or finding the speed with which the rocket leaving the Earth to enter the outer space must be sent, i.e. the escape velocity. In this section we shall learn about the units that are used to define the measure of rate of change of motion of an object.

The basis considered for the measurement of rate of change of motion is time. As we can say, objects moving with different rate will take different amount of time to cover a given distance. Hence, one of the ways of measuring the rate of motion of an object is to find out the distance travelled by the object in unit time. This quantity is defined as speed.

## Speed

Speed is defined as the total distance travelled by an object per unit time. The SI unit of speed is metre per second, represented as m/s. Other units include centimeter per second (cm/s) and kilometer per hour (km/hr). Speed is a scalar quantity and is represented only in terms of its magnitude.

A moving object may not always be in a uniform motion i.e., the rate of change of position (speed) of the object may vary with time. In order to define the measure of the rate of motion of such objects, the concept of average speed is used.

## Average Speed

The average speed of an object is obtained by dividing the total distance travelled by the total time taken.

Average speed = Total distance travelled/Total time taken

Vav = s/t   where Vav is the average speed of the object, s is the total distance travelled and t is the total time taken.

For example, if an objects covers 4 m in 6 seconds, 6 m in 4 seconds and 7 m in 7 seconds, the average speed can be calculated as

V (average speed) = Total distance travelled/ total time taken

V = (4+6+7) m / (6+4+7)s

V = 17/17 m/s = 1 m/s

The rate can be defined more comprehensively if we specify the direction of motion along with the speed. The quantity that takes both these into consideration is termed as velocity.

## Velocity (Rate of change of position)

Velocity is a vector quantity that is defined as the rate of change of position of an object with respect to a frame of reference with respect to time. Velocity is equivalent to the speed of the object along with the direction of motion. Velocity of an object can change with the change in speed and the direction of object. Speed and velocity have the same units, that is, m s–1 or m/s.

Most of us know that when an object is travelling along a straight line at a speed in a variable way, we could explain the capacity level of its rate of change of motion as per the terms of average velocity. This is calculated in similar manner like we calculate the   average speed. If in case the velocity of the object is fluctuating at a rate that is uniform, then average velocity would be calculated by the initial velocity’s arithmetic mean and final velocity for a specified time period.

## Average Velocity

Average velocity = (initial velocity +final velocity)/2

vav = (u+v)/ 2 ,where, vavis the average velocity, u denotes the initial velocity and v is shown by the final velocity.

#### Practise This Question

What are the characteristics of uniform motion?