Motion JEE and NEET Notes : Physics .

MOTION 

• Mechanics :It is Branch of physics, which deals with the study of objects in rest and in motion. Means Statics : Study of objects at rest or in equilibrium.

• Kinematics : It is the study of motion of objects without considering the cause of motion.

• Dynamics : It is the study of motion of objects considering the cause of motion.

• Rest  : An object is said to be at rest if it does not change its position with time, with respect to its reference point.

• Motion : An object is said to be in motion, if it changes its position with time, with respect to its reference point.

• Point mass/Point object : An object is said to be a point mass, if during its motion it covers distance much greater than its own size.

• Rectilinear motion or linear motion: An object travels in a straight line. It is called rectilinear or linear motion.

• One Dimensional Motion: The position change of the object with time in one dimension can be described by only one coordinate. Example . A stone falling freely under gravity.

• Two dimensional motion or motion in a plane : For an object travelling in a plane having two coordinates say X and Y are required to describe its motion. Ex. An ant crawling over the floor.

• Three dimensional motion : An object travels in space. To describe motion of objects in three dimension require all three coordinates x, y and z. Example. A kite flying in the sky.

• Distance Or Path Length: The length of the actual path traveled by an object during motion in a given interval of time is called the distance traveled by that object or path length. It is a scalar quantity. Hence it can not be in negative like displacement. It is always depends on the path followed by an object.

• Displacement : It is the shortest distance between the initial and final position of an object and it is directed from the initial position to the final position so it is a vector quantity. Hence displacement can be positive, negative or zero. It is not depend on the path followed by an object.

• Speed-
• It is the distance traveled per unit time by an object. It is a scalar quantity. It cannot be negative.

• Uniform speed : An object is said to be moving with a uniform speed, if it covers equal distances in equal intervals of time.

• Non-uniform speed : If an object is said to be moving with a Non-uniform speed, covers unequal distances in equal interval of time or equal distances in unequal interval of time.

• Instantaneous speed : The speed of an object at a particular instant of time is called the instantaneous speed.
  V inst =

• Average speed : It is ratio of the total distance traveled by the object to the total time taken. It cannot be zero.
  

• Dimensions : [ M0 L T-1] Unit : In SI systems.

• Velocity-
• It is the displacement of an object per unit time. It is a vector quantity. It can be positive negative  or zero.

• Uniform velocity :  An object is said to be moving with a uniform velocity, if it covers equal displacements in equal intervals of time.

• Non-uniform velocity : An object is said to be moving with a non uniform velocity, if it covers unequal displacements in equal interval of time or equal displacements in unequal interval of time.

• Instantaneous velocity : The velocity of an object at a particular instant of time is called the instantaneous velocity.

  

• Average Velocity : It is ratio of the total displacement to the total time taken. It can be zero.

  

• Dimensions : [M0 L T–1]. Unit : In SI system, m/s.

• Acceleration-

The rate of change of velocity with respect to time is called acceleration. It is a vector quantity.

Let velocity changes by during some interval of time .

Average acceleration is given by

Instantaneous acceleration is given by

SI unit is meter/sec2 (ms–2).

A body moving with uniform velocity has zero acceleration. It means that neither its speed nor its direction of motion is changing with time

• Uniform acceleration : If the velocity of the body changes in equal amount during equal time interval, then the acceleration of the body is said to be Uniform Acceleration. It is uniform when neither its direction nor magnitude changes with respect to time.

• Variable or non-uniform acceleration : If the velocity of body changes in different amounts during equal time interval, then the acceleration of the body is known as variable acceleration or non-uniform Acceleration. It is variable if either its direction or magnitude or both changes with respect to time.

Equations for Uniform Acceleration-

When the motion is uniformly accelerated i.e., when acceleration is constant in magnitude and direction :

• v = u + at.
• 

• v2 – u2 = 2as
• where u = initial velocity
  v = final velocity

  a = uniform acceleration
  s = distance traveled in time t.
• 
• Distance traveled in nth second
• sn = ;
• sn = distance covered in nth second

Vertical Motion Under Gravity-

• For a body thrown downward with initial velocity u from a height h, the equations of motion are,

v = u +gt

• If initial velocity is zero, then the equations are,

v = gt

• When a body is thrown upwards with initial velocity u, the equations of motion are,

v = u – gt

v2 = u2   2gh

 While using equations of motion we can have two conditions,

Condition 1 :

• a = +ve when velocity increases and
• a = –ve when velocity decreases.
• Take rest of physical quantities such as u, v, t and s as positive.

Condition 2 :

• Assume one direction to be positive and other negative.
• Assign sign to all the vectors (u, v, a, s),
• +ve sign is given to a vector which is directed to the positive direction and
• - ve sign is given to a vector which is directed to the negative direction.

Graphs related to Motion-

• Displacement Time Graph

• For a stationary body (v = 0) the time-displacement graph is a straight line parallel to time axis.

• When the velocity of a body is constant then time-displacement graph will be an oblique straight line. Greater the slope of the straight line, higher will be the velocity.

• If the velocity of a body is not constant then the time-displacement curve is a zig-zag curve.

• For an accelerated motion the slope of time-displacement curve increases with time while for decelerated motion it decreases with time.

• When the particle returns towards the point of reference then the time-displacement line makes an angle θ > 90° with the time axis.

• Velocity Time Graph

• When the velocity of the particle is constant or acceleration is zero.

• When the particle is moving with a constant acceleration and its initial velocity is zero.

• When the particle is moving with constant retardation.

• When the particle moves with non-uniform acceleration and its initial velocity is zero.

• When the acceleration decreases and increases.

• The total area enclosed by the time - velocity curve represents the distance travelled by a body.

While finding displacement through v – t graph, keeping sign under consideration.

Acceleration Time Graph-

• When the acceleration of the particle is zero.

• When acceleration is constant

• When acceleration is increasing and is positive.

• When acceleration is decreasing and is negative

• When initial acceleration is zero and rate of change of acceleration is non-uniform

• The change in velocity of the particle = area enclosed by the time-acceleration curve.