Kinematics notes 11th Physics CBSE

Kinematics in physics referes to the study of objects in motion without considering the cause of motion, i.e. the force or the inertia. The study involves taking into account the physical quantities such as, displacement, velocity position, coordinate axes, and time. The utmost important is the direction of motion. Without considering direction of motion we cannot solve the equations of motion faithfully, it may involve error in calculation. Best tool to consider the direction of different quantities is to consider them as vector quantities, and express them in unit vectors, such as i, j and k. These are the three components of the vector, alogn x, y and z axis. While we take the tuitions for class 11th physics, we do consider the more focus on numericals and problem solving. The problems from IIT, JEEmains, and advnced are to be taken into account. Coaching for 11th class CBSE physics can be done using the notes provided.

Download Notes for Kinematics

Kinematics: It is the branch of physics which deals with study of motion of objects without taking into account the factors, which cause motion. [Factors such as force, nature of bodies etc.]

Motion: An object is said to be in motion if it changes its position with time, with respect to certain fixed frame of reference [ i.e. surroundings]

e.g. A man walking on a road, bird flying in air, train moving on rails, etc.

Rectilinear motion: The type of motion in which a particle or a body moves along a straight line.

For example a car moving along straight road is in rectilinear motion.

Concept of point mass object:

Whenever a body covers very large distances as compared to its own size, then it can be treated as point mass object.

For example a car traveling a distance of 100 km, can be considered as point mass object.

Hence an object can be considered as a point mass object if during motion in a given time, it covers distances much greater than its own size.

Motion in one dimension:

Position of a body is always represented with the help of three coordinates, namely x, y and z coordinates.

If a body moves in such a way that during motion one out of three coordinates specifying position of object changes with time then it is said to be having one dimensional motion.

All kinds of motion along straight line are examples of one dimensional motion e.g. motion under gravity [free fall], motion of a car moving along straight road, motion of a train along straight rails etc.

Path length or distance:

The length of the actual path traversed by an object during motion in a given internal of time is called distance traveled by that object.

 

Suppose an object goes from A to D along the path shown in fig, then the distance traveled by object is given by AB+BC+CD.

Properties: (1) It is scalar, i.e. has no direction.

(2) It is always positive i.e. can never be negative.

(3) SI units Metre.

Displacement:

It is the change in position of the object in given time interval, and gives a vector drawn from the initial position to its final position.

From fig. displacement traveled by object is the vector joining A to D i.e.

Properties:

• Displacement is a vector quantity i.e. has both direction and magnitude.
• Displacement of an object in a given interval of time can be positive, negative or zero.
• Magnitude of displacement of an object between any two point gives the shortest distance between them.
• It has SI units of length i.e. m
• It follows sign convention.

SPEED

It is equal to rate of change of position of the object during motion along any direction.

Practically speed is given by distance traveled per unit time taken by body.

 

Properties:

• speed is a scalar quantity.
• Speed is always positive and can never be zero.
• Its SI unit is m/s or ms^-1.

Uniform speed: If a body covers equal distances in equal intervals of time then it  is said to be having uniform speed.

For example a train moving with constant speed on straight rails.

Variable speed: If a body covers unequal distances in equal intervals of time or vice versa.

For example a car moving on a busy road has variable speed.

Average speed: Whenever a body moves with variable speed then we need to consider its average speed.

Average speed of a body is defined as the ratio of total distance traveled by body to the total time taken during its jouney.

Thus

Instantaneous speed:

Speed of a body at any particular instant of time is called its instantaneous speed.

It is given as the ratio of very small distance traveled to very small time taken.

ds = very small distance, dt = very small time interval.

VELOCITY

Velocity of an object is defined ad the rate of change of its displacement from a given reference.

It given as displacement traveled by object per unit time taken between any two points.

 

Properties:

• velocity is a vector quantity i.e. has both direction and magnitude.
• Velocity of object can be positive, negative or zero.
• It follows sign convention.
• Its SI unit m/s or ms^-1.

Uniform velocity: An object is said to be having uniform velocity if it covers equal displacements in equal intervals of time.

If an object is having uniform velocity then it is said to be having uniform motion.

Variable velocity:

If the object covers unequal displacement in equal intervals of time or vice versa then it is said to be having variable velocity.

Average velocity:

Whenever a body is moving with variable velocity then we need to consider its average velocity.

Average velocity is the ratio of total displacement traveled to total time taken by body to cover that displacement.

 

POSITION TIME GRAPH OR X-T GRAPH

The graphical relation between displacement from a given reference and time is called x-t graph or position time graph.

 

• Position time graph for a body at rest.

If a body is at rest then its displacement is not changing with time. Thus if a body is at rest then its x-t graph is always a straight line parallel to time axis.

• Position time graph for a body in uniform motion.

If a body is in uniform motion then it covers equal displacement in equal intervals of time. So that its x-t graph is a straight line.

Consider any two points A and B with coordinates (x₁, t₁) and (x₂, t₂) respectively.

Let . Then from right triangle ACB we have

 

but Tanθ represent slope of the line, thus.

Hence slope of x-t graph represent velocity of object.

 

• Position time graph for a body in uniformly accelerated motion:

If a body is having uniformly accelerated motion or positive acceleration then its x-t graph will be parabolic.

• Position time graph for a body in retardation:

If a body is having negative acceleration then it has its x-t graph as decreasing parabola.

VELOCITY TIME GRAPH

Graphical relation between the velocity of object and time taken is called v-t graph.

• Velocity time graph for a body at rest.

If a body is at rest then its velocity will be zero. Thus velocity of object will always be zero irrespective of time interval. Hence its v-t graph is a straight line coincident with time axis.

• Velocity time graph for a body in uniform motion.

If a body has uniform motion then it has constant velocity, which does not change with time. Thus velocity time graph will be straight line parallel to time axis.

• Velocity time graph for a body in uniform accelerated motion.

If a body has uniformly accelerated motion then its velocity increases by equal amount in equal intervals of time.

 

• V-t graph for a body in retardation.

v-t graph for a body in negative acceleration i.e. retardation is also a straight line.

 

 

 

 

 

 

 

 

 

 

 

 

(UNIFORM MOTION)

1. State in the following cases whether the motion is one two or three dimensional motion:

• a kite flying on a windy day
• a speeding car on a long straight highway
• a carom coin rebounding from the side of the board
• A planet revolving around its star.

1. A particle is moving along a circular track of radius r. What is the distance traversed by the particle in half revolution? What is displacement?
2. Two straight lines drawn on the same displacement time graph make angles 30⁰ and 60⁰ respectively. Which line represents the greater velocity? What is the ratio of the two velocities? [1:3]
3. A ship moves due east at 12 km/hr for one hour and then turns exactly towards south to move for an hour at 5 km/hr. Calculate its average velocity for the given motion.  [6.5km/hr; 22^o37’south of east]
4. A car travels along a straight line with speed 40 km/hr from A to B and returns back from B to A wit speed 60 km/hr. find the average speed of the car and its average velocity.   [48km/hr; 0]
5. A car traveled the first third of a distance x art a speed of 10 km/hr, the second third at a speed of 20 km/hr, and the last third at a speed of 60km/hr. Determine the average speed of the car over the entire distance x.  [18km/hr]
6. A particle moves along a circle of radius R. It stars from A and moves in anticlockwise direction. Calculate the distance traveled by the particle (a) from A to B (b) from A to C (c) from A to D (d) in one complete revolution. Also calculate the displacement in each case.

 

 

 

 

1. A car travels a distance A to B at a speed of 40 km/hr and returns to A at a speed of 30 km/hr (i) What is the average speed for the whole journey?(ii) What is the average velocity?  [34.3 km/hr; 0]
2. A car travels along a straight line for first half time with speed 40 km/hr and the second half with speed 60 km/hr. Find the mean speed of the car. [50km/hr]
3. A car is moving along a straight line say OP (in following fig). It moves from O to P in 18 sec and returns from P to Q in 6 sec. What are the average velocity and average speed of the car in gong (a) from O to P? And (b) from to P and back to Q?