💢 Motion in a straight line
What is motion ?
It is defined as change in position of an object with time.
Example -: The sun is itself is in motion in the milky way galaxy and milky galaxy is again is in motion within its local group of galaxies.
What is rectilinear motion ?
The motion of an object along a straight line is called as rectilinear motion . ex-: a car moving on a straight line.
Note -: In kinematics we study a way to describe motion without going into the causes of motion.
What is path length ?
The distance covered by an object on any path is called path length.
Example -: if a man start from home and reached to his office then the path length is equal to total distance cover by that man in reaching his office.
Here the path length cover by man = 200 m
fig 1.
👉path length = distance covered
What is displacement ?
The shortest length of path covered by the object is called displacement.
👉 The magnitude of displacement may or may not be equal to the path length covered by an object.
In this diagram the displacement = path length (distance).
In the fig . 1 -: if we connect A and F then displacement is the length between the A and F . 👉 In fig. 1 displacement is not equal to the distance covered by an object.
In this figure displacement = length of AF
👉 Displacement depend upon the initial and final position of object during the motion. 👉 we can find the displacement only by finding the distance b/w the initial and final state of object during the motion .
What will be the displacement in the above diagram ?
sol -: first of all join A and D then apply the pythagoras theorem.
in right angle triangle AEF
h*h = p*p +b*b
AF*AF = AE*AE +EF*EF = 100*100 +120*120
= 10000 + 14400
= 24,400m*m
AF = √24400 m* m = 156.20 m
This is the displacement of object in the above diagram.
What is uniform motion ?
If an object moving along the straight line covers equal distances in equal interval of time , it is said to be in uniform motion along a straight line.
What is velocity ?
It is defined as the rate of change of position vector w.r.t. time .
👉It is a vector quantity i.e. having magnitude as well as specific direction .
Ex -: 40m/s north.
What is Average velocity ?
It is defined as ratio of change in position and time interval in which the displacement occur.
Avg. velocity = Δx/Δt = x2- x1 / t2- t1
What is average speed ?
It is defined as the ratio of total path travelled by an object to the total time interval during which the motion has taken place.
Avg.speed = total path travelled/ total time interval
The s.i. unit of average speed = m/s
Note -: if the motion of object is in straight line and in the same direction then the magnitude of average velocity is equal to magnitude of average speed. but it is not alway same in all case.
What is speed ?
It is defined as the rate at which an object cover any distance. It is a scalar quantity (having magnitude only ) .
speed = Distance/ time .
It's unit is m/s .
What is instantaneous speed ?
The magnitude of instantaneous velocity is called instantaneous speed.
What is instantaneous velocity ?
The velocity at an instant is defined as the limit of average velocity becomes infinitesimally small. The direction of instantaneous velocity is always tangent to the path.
What is accleration ?
It is the rate of change of velocity w.r.t. time.
It's s.i. unit is m/s*s .
👉 the change in velocity with time is the main causes of acceleration .
What is average acceleration?
It is defined as average change of velocity per unit time.
avg. acceleration=final velocity -initial velocity / final time - initial time.
What is instantaneous acceleration?
The acceleration of the object at some particular instant of time is called instantaneous acceleration.
instantaneous acceleration = dv/dt .
💢position-time graph for uniform motion of an object .
positive accleration graph
👇
Zero acceleration graph
💥 Graphical analysis of one- dimensional motion
1. position- time graph The slope of position - time graph give the velocity.
dx/dt = velocity
The slope of tangent on position - time graph give the instantaneous velocity.
Graph no-: 2
👉The slope of tangent in the graph 2 will give the average velocity. Average velocity in going from (t1 ➝t2)
= Δx/Δt = xf - xi /tf- ti
I hope this will helpful for you
please comment and share so that many one get benefited.
SUMAN KUMAR
fig 1. 
The slope of position - time graph give the velocity.
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