MOTION CLASS 9
Ch-8 Motion
✤ Motion: An object is said to be in motion when its position changes
continously with the respect of time.
Ex → flying birds, swimming fishes, etc
✤ Physical Quantity: All those quantities which can be measured
Ex → Length, mass, temperature, force, pressure, etc
Physical Quantity
Scalar Quantity
vector quantity
✤ Scalar Quantity ✤ Vector Quantity
(i) These are not depend on
direction
(ii) It can be described only by
magnitude
(iii) Ex-length, mass, time
temperature, density
* Distance and displacement
✤ Distance → It is the actual length of the path covered by an object
irrespective of the direction.
* Distance is a scalar quantity.
✤ Displacement :- The shortest distance between the initial position and
final position of the body along with direction is known
as displacement.
* Displacement is a vector quantity.
⇒ Distance can't be zero (0)
⇒ Displacement can be zero (0)
✤ Speed :- The distance travelled by an object per unit time.
Speed = Distance/time
S.I unit = m/s
* Speed is a scalar quantity
✤ Velocity:- Velocity of a body is the distance travelled by it per unit time in
given direction.
* velocity is a vector quantity.
V = displacement / time
S.I unit = m/s
✤ Uniform and Non-Uniform motion
✤ Uniform motion : When the body travels equal distance in equal
interval of time it's called uniform motion.
✤ Non-uniform motion: When the body travels unequal distance in equal
interval of time it's called non-uniform motion
→ Average speed = Total distance covered / total time taken
→ Average velocity = (Initial + final velocity) / 2
✤ Uniform velocity :- A body has a uniform velocity if its travel in a
specified direction in a straight line and moves over equal
distance in equal interval of time.
* velocity of an object can be changed in two ways :-
* By changing the speed of the body
* By keeping the speed constant but by changing the direction.
✤ Acceleration:- Rate of change of velocity of a body with respect to time
or (change in velocity per unit time)
a = v - u / t u -> Initial velocity
v -> final velocity
t -> Time taken
s -> Distance
a -> Acceleration
✤ Uniform Acceleration:- when an object travels in a straight line and its
velocity increases or decreases by equal amounts in
equal interval of time. This is known as uniform
acceleration.
Note :- To convert km/h to m/s
-> km/h x 5 / 18
Note :- To convert m/s to km/h
-> m/s x 18 / 5
✤ Difference between distance and displacement
✤ Distance
* It is the actual path length
covered by an object.
* It can never be 0
* It is scalar quantity
✤ Difference between speed and velocity.
✤ Speed
* Distance travelled by a body
per unit time
* It is scalar quantity
* It is always positive
Graph
* Graph provides a convenient method to represent basic information
about variety of event.
* To describe the motion of an object we can use line graphs
(i) Distance time graph
* Time in x-axis
* Distance in y-axis
* Uniform motion :- straight line in graph
* Non-uniform motion:- Curved line in graph
→ Distance time graph shows the change in distance of a body from a fixed
point on the position with time
Distance - time graph for stationary Object
Distance time graph for uniform motion
Time(s)
Speed of body from A to B
Speed = (s_2-s_1)/(t_2-t_1 )= (40-20)/(40-20)= 20/20
= 1m/s
Disntance time graph for non-uniform motion
It shows object at non-uniform
motion.
✤ Velocity time graph
→ Distance time graph gives speed.
→ velocity time graph gives acceleration.
→ Displacement time graph gives velocity.
Straight line but not uniform
motion because velocity is not
constant.
✤ Distance in velocity time graph
Displacement => velocity X time => 10 X 6 = 60 m
Area of Rectangle => L X B = 10 X 6 = 60 m
ABCD is a trapezium
Area of Trapezium = Displacement
Uniform retardation (Negative Acceleration) because initial speed is not zero.
Non- Uniform acceleration
Equation of Motion by Graphical Method
* First equation of motion
* Let us consider as object moving with initial velocity (u) time (t). it
attains final velocity (v) covering distance (s) with uniform acceleration
(a).
OA = u
BC = v
BD = v-u
OC = t
Acceleration = v-u / t
a = (BC-BD) / OC = BD / OC
a / 1 v-u / t = at = v-u
v = u+at
Equation of velocity - time relation
* Second Equation of Motion
S = Area under the graph
S = Area of rectangle (OADC) + Ar of (Δ ABD)
= OA x OC + ½ x AD x BD
S = ut + ½ (t) (v-u)
Putting the value of v-u from eq ①
S = ut + ½ (t) (at)
S = ut + ½ at²
Equation of position - Time relation
* Third equation of motion
S = Area under the graph
S = Area of trapezium
S = ½ (Sum of parallel sides) x height
S = ½ (BC + OA) x OC
S = ½ (v+u) (t)
Putting the value of t from eq ①
S = ½ (v+u) (v-u)
2as = v²-u²
Circular motion :-
→ When an object moves in a circular path with uniform speed, its motion
is called uniform circular motion.
→ Time taken by moving object on circular path is different for different
revolutions OR Revolution per unit - time is not constant
* * * * * * * * * * * * * * *
