Motion
★ motion :- change in in position of an object with respect to time and frame of reference.
★ Types of motion :-
On the basis of direction
1) one dimensioned motion :- when an object moving in a straight line in a plane.
2) two dimensioned motion :- when an object moving along a curved path in a plane.
3) three dimensioned motion :- when an object randomly in space.
On the basis of state of motion
1) uniform motion :- when a body covers equal distance in equal interval of time.
Its distance time graph for a body is straight line.eg :- hands of water,rotation of earth etc.
Its distance time graph for a body is curved line.eg :- freely falling body.
It is a scalar quantity.
Speed = distance travelled
Time taken
s= u
t
SI unit of speed is metre per second = m/s = m\ s^{-1}
★ types of speed :-
1) uniform speed ( constant speed ) :-
When I have body cover equal distance in equal interval of time.eg :- movement of earth about its crust.
2) non-uniform speed :- when ab body covers an equal distance in equal interval of time.eg :- freely falling body.
3) Average speed :- it is obtained by dividing the total distance travelled by total time taken.
Average speed = total distance travelled
total time taken
Average speed is a scalar quantity.
Average speed never be negative zero.
4) Instantaneous speed :- the speed of a body at a particular instant of time is called its instantaneous speed.
★ Velocity :- the rate of change of displacement of a body.
It is a vector quantity.
Velocity = displacement
Time
V = s
t
SI unit of velocity is metre per second = m/s.
Note :- when the position of a body always in a particular direction the speed is devoted by the velocity.
★ Types of velocity :-
1) uniform Velocity ( constant velocity ):- when a body travels in a particular direction and moves over equal distance in equal interval of time.
2) Non-uniform velocity (variable velocity):-
when a body travels in a particular direction and moves over an equal distance in equal interval of time.
OR
When a body travels equal distance in equal interval of time but changes its direction is also as noun as non uniform velocity.
Eg:- moving a car with uniform speed in circular path.
3) Average velocity:- the ratio of total displacement to the total time taken.
Average velocity = total displacement
Total time taken
Q1. A car travels 30 km at a uniform speed 40 km per hour and 30 km at a uniform speed of 20 km per hour find its average speed.
Sol:- 
Q2. A boy walks to his school at a distance of 6 km with constant speed of 2.5 km per hour and walks back with a constant speed of 54 km per hour is average speed and average velocity for round trip expressed in km per hour.
Sol:-
★ Acceleration :- the rate of change of velocity is called acceleration.
Acceleration = change in velocity
time taken
a = v- u
t
V= acceleration of the body.
u= initial velocity of the body.
t= time taken for the change in velocity.
a= acceleration of the body.
It is a vector quantity.
SI unit of acceleration is metre per second square = m / s2.
In velocity time graph acceleration is determined by the slope of the graph.
Fan Q = dv
dt
★ Types of acceleration :-
1) uniform acceleration:- if a body travels in a straight line and its velocity increases by equal amounts in equal interval of time then it is said to be in a state of uniform acceleration.
Eg :- motion of freely falling body.
Velocity time graph of uniform acceleration motion is straight line.
2) non-uniform acceleration:- if a body increases its velocity by an equal amount in equal interval of time.
Eg:- motion of bus in crowded area.
Velocity time graph for uniform acceleration motion is curved line.
3) Instantaneous acceleration:- the acceleration of a body at the instant is instantaneous acceleration.
4) Retardation or deceleration or negetive acceleration:- the rate of decrease of velocity.
Q1. A boy driving a car with a speed of 80 metre per second and applies the break after 4 second the car stop. find the retardation?
Sol:-
Q2. A ship is moving at a speed of 56 km per hour one second later it is moving at 58 km per hour what is its acceleration.
Sol:-
Q3. A train starting from a railway station and moving with uniform acceleration attains a speed of 40 km per hour in 10 minutes find its acceleration?
Sol:-
1) Distance-time graph :- 10 public stands time graph indicates speed.
a) uniform speed:- if the distance time graph of a body is a straight line then its speed is uniform.
b) non-uniform speed:- if the distance time graph of a body is curved line its speed is non uniform.
2) Velocity time graph :- i the slope of velocity time graph gives acceleration.
The area velocity time graph gives distance covered.
a) when velocity is constant :- if velocity is constant then acceleration is zero.
Note:- to find the distance travelled from this type of graph we have to find the area inclosed.
b) when velocity changes uniformly.
Acceleration = change in velocity
Time taken
Acceleration = AB
OB
Distance = area of the ∆OAB
= 1/2×OB×AB
c) when initial velocity is not zero.
Area of trapezium DABC =1/2(OA+BC)×OC
Acceleration = change in velocity
Time taken
Acceleration = BC-OA
OC
a = v- u
t
d) when velocity changes non-uniformly.
When velocity changes uniformly then acceleration is non uniform acceleration.
Q1. Hindi given figure what type of motion is represented by the path AB,BC,CD,DE.
Sol:- AB --> uniform velocity increase ⬆️
BC --> constant velocity, a= 0
CD --> uniform velocity ⬆️
DE --> uniform Velocity ⬇️
Q2. The velocity time graph of a moving body is shown in figure calculate the following.
1) first equation of motion ( v=u+at )
OA=u
BC=v.
OC=t
BC=BD+DC
v=BD+u -------1.
Now acceleration = slope of graph
= BD
AD
a= BD (AD=OC=t)
t
at = BD -------2.
Putting the value of equation 1 on equation 2 their,
v=BD+u
v=at+u
v=u+at
2) second equation of motion
( s=ut+1/2at2 )
Suppose the body travels a distances in time t.
The distance travelled by the body is given by the area of a space between the AB and time at time axis OC.
Distance travelled = area of under the graph.
S= area of rectangle OA& BC + area of ∆ABD.
S= OA×OC+1/2×AB×BD
S= u×t+1/2×t×BD ------>1.
°° DA=u
OC=t
AD=OC=t
Slope of the graph= BA
AD
( °° AB=OC=t )
a= BD
t
BD=at ----->2.
Putting the value of equation 1 in equation 2
s=ut+1/2t×BD
s=ut+1/2×t×at
s=ut+1/2at2
3) third equation of motion ( V2 = V2 + 2as )
★ Circular motion
When a body moves in such a way that its distance from a fixed point always remains constant then it's more than its to be circular motion.
1) uniform circular motion :- when a body moves in a circular pattern with uniform speed its motion is called uniform circular motion.
OR
Is the radius vector sweep out equal angles in equal time than its motion is said to be uniform circular motion.
In uniform circular motion speed remain constant velocity change due to this direction not magnitude.
Due to change in velocity motion along a circular path is to be accelerated.
Circular motion is balance by two forces
a) centrifugal force
b) centripetal force
Direction of motion of a body moving in a circular path act away instant is about a tangent to the position of the body on the circular path at work instant of time.
This blog is edit by khubaibul Islam
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