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Class 9, Science, Chapter-7, Lecture-2, Speed and Velocity (Notes)

UNIFORM MOTION:

The motion of a body which travels equal distances in equal intervals of time in a straight line is called uniform motion.

NON-UNIFORM MOTION:

The motion of a body which travels unequal distances in equal intervals of time or equal distances in unequal intervals of time or changes direction is called non-uniform motion.

SPEED:

The rate of change of position of an object with respect to time is called its speed.
Speed is denoted by v

Mathematically ${\rm{v = }}{{{\rm{\delta s}}} \over {{\rm{\delta t}}}}$

where

${\rm{\delta s =  change~in~position}}$

${\rm{\delta t =  time~taken}}$

  • Speed is SCALAR quantity
  • SI unit of speed is metre per second ( m/s or ${\rm{m}}{{\rm{s}}^{ - 1}}$)
  • cgs unit of speed is centimetre per second ( cm/s or ${\rm{cm}}{{\rm{s}}^{ - 1}}$)
  • commonly used unit is kilometre per hour ( km/h or ${\rm{km}}{{\rm{h}}^{ - 1}}$) 

RELATIONSHIP BETWEEN ${\rm{km}}{{\rm{h}}^{ - 1}}$ and ${\rm{m}}{{\rm{s}}^{{\rm{ - 1}}}}$ :

$$1{\rm{km}}{{\rm{h}}^{ - 1}} = {{1{\rm{km}}} \over {1{\rm{h}}}} = {{1000{\rm{m}}} \over {60 \times 60{\rm{s}}}}$$

$$ = {{1000} \over {60 \times 60}}{\rm{m}}{{\rm{s}}^{ - 1}}$$

$$ = {5 \over {18}}{\rm{m}}{{\rm{s}}^{ - 1}}$$

$${\rm{1km}}{{\rm{h}}^{ - 1}} = {5 \over {18}}{\rm{m}}{{\rm{s}}^{ - 1}}$$

 

$${\rm{1m}}{{\rm{s}}^{ - 1}} = {18 \over {5}}{\rm{km}}{{\rm{h}}^{ - 1}}$$

 

UNIFORM SPEED:

The speed of a body which travels equal distances in equal intervals of time is called uniform speed.

INSTANTANEOUS SPEED:

The rate of change of position of a body with respect to time at a particular instant of time is called instantaneous speed.

Mathematically ${\rm{v = }}{{\rm{d}} \over {{\rm{dt}}}}{\rm{s}}$

where

${\rm{s =  change~in~position}}$

${\rm{t =  time~taken}}$

AVERAGE SPEED:

The total distance travelled by a particle divided by the total time taken to cover the distance is termed as average speed.

Average speed is denoted by  ${{\rm{v}}_{ave}}$  or  $\overline {\rm{v}} $

Mathematically   $\overline {\rm{v}}  = {{\rm{s}} \over {\rm{t}}}$

where

${\rm{s =  total ~distance}}$

${\rm{t =  total ~time~taken}}$

VELOCITY:

The rate of change of position with respect to time in a specific direction is called velocity.

Velocity is denoted by $\overrightarrow {\rm{v}} $

Mathematically ${\rm{v = }}{{{\rm{\delta~~ \overrightarrow{s}}}} \over {{\rm{\delta~~ \overrightarrow{t}}}}}$

where

${\rm{\delta~~ \overrightarrow{s} =  change~in~position}}$

${\rm{in~a~specific~direction}}$

${\rm{\delta~ t =  time~taken}}$

  • Velocity is VECTOR quantity
  • SI unit of velocity is metre per second ( m/s or ${\rm{m}}{{\rm{s}}^{ - 1}}$)
  • cgs unit of velocity is centimetre per second ( cm/s or ${\rm{cm}}{{\rm{s}}^{ - 1}}$)
  • commonly used unit is kilometre per hour ( km/h or ${\rm{km}}{{\rm{h}}^{ - 1}}$) 

UNIFORM VELOCITY:

The velocity of a body which travels in a straight line and covers an equal distance in equal intervals of time is called uniform velocity or constant velocity.