Motion

Tutormate > CBSE Syllabus-Class 9th Physics > Motion

03 Speed and Velocity

SPEED

Speed of a body is the distance travelled by it per unit time.
It is represented as:

S p e e d = \frac{D i s \tan c e t r a v e l l e d}{t i m e t a k e n}

v = \frac{s}{t}

The SI unit of speed is meters per second represented as m/s. Derived units are cm/s and km/hr.
Speed is a scalar quantity: Speed has magnitude only, it has no specified direction, and therefore, speed is a scalar quantity.
An object may not always be in a uniform motion. In other words, the rate of change of position (speed) of the object may vary with time. In such cases, average speed is used to measure the rate of motion of such objects.
Odometer: It is an instrument installed in car, which measures the distance travelled by a car.

AVERAGE SPEED

The average speed of a body is the total distance travelled divided by the total time taken to cover this distance.
Average speed is represented as:

A v e r a g e s p e e d = \frac{T o t a l d i s \tan c e t r a v e l l e d}{T o t a l t i m e t a k e n}

EXAMPLE: If an objects covers 7 m in 6 seconds, 6 m in 4 seconds and 4 m in 7 seconds, the average speed can be calculated as

V = \frac{(4 + 6 + 7) m}{(6 + 4 + 7) s} = \frac{17}{17} = 1 m / s

UNIFORM SPEED (OR CONSTANT SPEED)

A body has a uniform speed if it travels equal distances in equal intervals of time, no matter how small these time intervals may be.

VELOCITY

Velocity of a body is the distance travelled by it unit time in a given direction.
Velocity is represented as:

V e l o c i t y = \frac{D i s \tan c e t r a v e l l e d i n a g i v e n d i r e c t i o n}{T i m e t a k e n}

The SI unit of velocity is metres per second (m/s or ms^-1).
Velocity has magnitude as well as direction. Hence velocity is a vector quantity.

Average velocity

Average velocity is the rate at which an object changes its position from one place to another.
If the velocity of the object changes at an uniform rate, average velocity would be calculated by the initial velocity’s arithmetic mean and final velocity for a specified time period.

O r, A v e r a g e v e l o c i t y = \frac{I n i t i a l v e l o c i t y + F i n a l v e l o c i t y}{2}

v_{a v} = \frac{(u + v)}{2}

w h e r e, v_{a v} i s t h e a v e r a g e v e l o c i t y,

u i s t h e i n i t i a l v e l o c i t y a n d

v i s t h e f i n a l v e l o c i t y .

Uniform Velocity (or Constant Velocity)

A body has a uniform velocity if it travels in a specified direction in a straight line and moves over equal distance in equal intervals of time. The velocity of a body can be changed in two ways: