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Compton Scattering

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 Q. A photon traveling in the positive x-direction collides with a stationary free electron. The incident photon has a wavelength of 0.0310 nm. Post-collision, the electron moves at an angle 𝛼 below the positive x-axis, and the photon deflects at an angle 𝜃 = 66.3° above the positive x-axis. A) Calculate the angle 𝛼 (in degrees). B) Compute the velocity of the electron (in m/s). Solution: 
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Motion in Straight Line

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Motion in Straight Line:
Motion in straight line is defined as motion in one dimension (1-D). It is also known as linear motion. It can be participated in two parts -
(i) uniform linear motion and 
(ii) non-uniform linear motion

Uniform Linear Motion:
In this motion a body covers equal distance in equal time intervals i.e. velocity along the path is constant. In this motion a body moves with a constant acceleration. 
Non-uniform Linear Motion:
In this motion a body moves with a variable velocity in a given interval of time.

Equation of Motion with constant Acceleration:
Consider that a particle has constant acceleration 'a'. It's initial velocity is 'u' and final velocity is 'v' after 't' time. Now acceleration can be written as: dv/dt = a  
Particle covers 's' distance or displacement (since particle is moving along the straight line) in time 't'. From 1st equation-

write equation 1st again-
Displacement of Particle in nth second:
From 2nd equation-
Example 1: A car started from rest and moves with a constant acceleration 2m/s². Find the following-
(i) velocity of the car after 4s  ?
(ii) total distance covered by the car in 8s ?
(iii) what is the displacement of the car if it's displacement is 36m
Example 2: A particle has constant acceleration 0.5 m/s². Find its displacement in 5th and 8th second ?

Free Fall:
Free fall is the most common example of the motion in straight line. A free falling object is an object that is falling under the influence of gravity. Gravitational acceleration is defined as 'g' and its value (9.8 m/s²) is taken as constant near the surface of the earth. We take vertically upward as positive direction, then if a particle, which has initial velocity u and final velocity is v, is falling from any height then motion of equations can be transferred as -
Example 3: A ball is thrown up with a initial velocity 5 m/s². Find maximum height attained by the ball ? (take g = 10 m/s²)
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