### __Kinematics Introduction and more…__

**1.The terms Rest & Motion are relative terms.**

- There is no object in the universe which is at
**absolute rest**.Ex: A text book in a book rack may be relatively at rest, with respect to the immediate surroundings. But, the earth is revolving around sun, therefore every particle on earth will be in motion including the text book.Hence, the text book also will be in motion with respect to Sun. - There is no object in the universe which is in
**absolute motion**. Ex:A person traveling in a train will be in motion as the train is moving.But, with respect to the fellow passengers and all the non moving objects in the train the person will be relatively at rest.

**2. The shortest distance between initial and final positions of a moving body is called its displacement.**

- Ex: If a object starts its journey from a point A, travels in a circular path and again reaches the point A. Then its displacement is Zero,because its initial and final points are same. But, the distance traveled is d = 2r = length of the circumference of circular path, i.e the distance (d) traveled by a object may not be equal to its displacement (S). When the object moves in a curved path or zig zag path d>S.
- If the object travels in a specified direction along straight line path from a point A to a point B. In this case the distance d=AB and displacement S=AD will have same magnitudes i.e d=S.
- Displacement is a vector and distance is a scalar quantity.
- An object started from rest,travels with uniform acceleration.Find the ratio of its displacements in ,,. . . . . seconds of its journey. ::: . . . . . . . . := 1:3:5: . . . . . . . . . : (2n-1).
- If body starts with an initial velocity u, and travels with uniform acceleration a .Find the ratio of its displacements in ,,. . . . . seconds of its journey. ::: . . . . . . . . := (2u+a) : (2u+3a) : (2u+5a) : . . . . . . . . . : {2u+(2n-1)a}.

**Speed (v)** : The distance traveled by a body in unit time is called Speed of the body.Speed is a scalar quantity.

**Velocity (v) ****: **Displacement of a body in unit time is called Velocity (or) Rate of change of displacement of a body is called its velocity. Velocity is a vector .

- Units: Both speed and velocity have same units. C.G.S unit is cm / sec;, F.P.S unit is ft / sec; & M.K.S (or) S.I unit is m / sec.
- Relation between magnitude of velocity and speed will be speed velocity.
- For a object moving in a circular path with a constant speed, the magnitude of velocity remains constant.But,the direction of motion the object continuously changes.
- Velocity of an object is said to be constant if a)its magnitude of velocity is constant and b)its direction of motion remains unchanged.
- If the velocity of an object is varying (not constant) such object will possess acceleration, i.e the condition for an object to possess acceleration is v constant.
- An object started from rest and traveling with uniform acceleration a.Find the ratio of velocities at the ,,. . . . . seconds of its journey.::: . . . . . . . . := 1:2:3: . . . . . . . . . : n.
- If body starts with an initial velocity u, and travels with uniform acceleration a .Find the ratio of its velocities at ,,. . . . . seconds of its journey. ::: . . . . . . . . := (u+a) : (u+2a) : (u+3a) : . . . . . . . . . : (u+na).

**Acceleration ( a )**: Rate of change of velocity of a body is known as its acceleration. (or) Change in velocity of a body in unit time is called its acceleration. Acceleration is a vector.

- Acceleration in a body may be due to a) change in magnitude of velocity of a body (or) b) change in direction of velocity of the body or c) change in both magnitude and direction of velocity of the body.
- Ex: For a vertically projected body or for a freely falling body the acceleration is due to change in the magnitude of velocity.
- Ex:For a body moving along a circular path with constant speed, the acceleration is due to change in the direction of velocity .
- Units : C.G.S unit is cm/ ; F.P.S unit is ft/ and M.K.S or S.I unit is m/ .
- Direction of acceleration : a) For freely falling body the direction of velocity and acceleration are same, in this case acceleration is considered to be positive( + ) b) For a body moving up vertically , direction of acceleration will be opposite to direction velocity of the body,in this case the acceleration is considered to be negative ( – ) c)For the body in circular motion the direction of acceleration will be perpendicular to the direction of velocity at every point.
- Acceleration of a body may not be zero, even if the velocity of the body is zero. Ex: For a vertically projected body , when it is at Maximum height its velocity becomes zero but its acceleration is equal to ” g “.

**Freely falling body**** ****:** Any object falling under the influence of gravitational force, with acceleration due to gravity is called freely falling body.

- Ratio of displacements of a freely falling body after 1sec,2sec, . . . . . . . . . . . . . . . . n sec of its journey will be 1 : 4 : 9 : 16 . . . . . . . . . .
- Ratio of displacements of a freely falling body 1st,2nd,3rd …… nth sec of its journey will be 1 : 3 : 5 : 7 : 9 . . . . . . . . (2n-1).
- Ratio of velocity of a freely falling body after 1 sec, 2 sec, 3sec , . . . . . . . . . . . . . . of its journey will be 1 : 2 : 3 : 4 :
- Ratio of velocity of a freely falling body after 1st , 2nd , 3rd , 4th . . . . . . . . . . . . . . . . . of its journey will be 1 : 1 : 1 : . . . . . . . . . . i.e its velocity in every interval is equal to “g”.
- For a freely falling body velocity will continuously change (Increases) and the acceleration ( g ) remains constant.

**Vertically projected up body**: For a body projected vertically up with an initial velocity u,

- Velocity at maximum height will be zero.
- At any point during its upward journey, direction of velocity will be opposite to direction of acceleration.
- Velocity of the object at any point in its path is same in magnitude,when it is going up and coming down.
- It reaches ground with the velocity(u) with which it is projected.
- Displacement in nth second of its up ward journey = u-
- For a vertically projected up body velocity will continuously change (decrease) and the acceleration ( -g ) remains constant.
- Ratio of velocity of a freely vertically projected up body after 1 sec, 2 sec, 3sec , . . . . . . . . . . . . . . of its journey will be :: . . . . . . . . . . . . : = (u-g) : (u-2g) : (u-3g) : . . . . . . . . . . . . . . : (u-ng).

**Projectile** : A body projected with an angle other than (≠ ) is called a projectile .

- Path of a projectile is parabola.
- For a projectile as no force acts on it in the horizontal direction, it does not possess acceleration in horizontal direction.
- The horizontal component of velocity remains constant through-out its journey.
- gravitational force acts on it vertically downwards,hence it will possess acceleration equal to acceleration due to gravity and vertical component of velocity will be different at different points.
- Path of a body projected horizontally from top of a tower is a parabola.
- Path of an object dropped from aeroplane flying at certain height will be a) parabola with respect to a stationary observer, but b) path of that object is a straight line with respect to an observer in the aeroplane.
- If a body is projected horizontally from the top of a tower and another body dropped freely from the same height at the same time, both will reach the ground at the same time.
- At maximum height of a projectile : a)It will possess only horizontal velocity b)Horizontal component of velocity = c)vertical component of velocity is = 0 d) K.E = e)P.E = f) velocity is minimum, hence K.E also will be minimum G) P.E is maximum as it is at maximum height.