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.