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Motion & Force

Introduction

The concept of state of motion a rest are described relative to the observer.

• If a body does not change its state wrt surrounding is in the state of rest.
• If a body changes its state wrt surrounding then its is in the state of motion.

A moving body can posses both state of rest and motion. depending on the observer.

Displacement

Displacement is a vector that depicts the change in the position of body from initial to final position.

Info

When a body moves along straight line then the displacement coincides with distance traveled.

Distance

The length of the path between two points is called distance.

Speed	Velocity
The ratio of distance covered by a body to the time taken is called speed.	Time rate of change of displacement is called velocity.
Scalar quantity	Vector quantity

Both have dimensions \([LT^{-1}]\) and are measured in \(ms^{-1}\).

Info

For a body moving with uniform speed, its instantaneous and average speeds are equal to each other.

Acceleration

Rate of change of velocity is called acceleration $$ a=\frac{\Delta v}{\Delta t} $$

Acceleration may be produced by the variation of:

• Magnitude of velocity ie speed.
• Direction of velocity.
• Both magnitude and direction of velocity.

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• Curve like \(OG\) where slope decreases with time it corresponds to decreasing acceleration.

  mising graph
  

• Curve like OE where slope increases with it corresponds to increasing acceleration.

Some Important points

• If a body moving with constant velocity then acceleration (or force on the body) is zero.
• The slope of \(d-t\) graph gives velocity.
• The slope of \(v-t\) graph gives acceleration.
• If a body falls freely or start from rest or is dropped \(v_i=0\).
• The velocity and acceleration need not to be in same direction.
• Velocity and acceleration need not to be zero simultaneously.
• When a body performs journey in two parts of equal distance with speed \(v_1\) and \(v_2\) then average speed $$ v_{av}=\frac{2v_1v_2}{v_1+v_2} $$
• When a body performs journey in two parts of equal time with speed \(v_1\) and \(v_2\) then, average speed $$ =\frac{v_1+v_2}{2} $$
• If the body is thrown upward then it will rise until its velocity becomes zero and will rise to a height $$ h=\frac{v^2}{2g} $$
• If a body travels with a uniform acceleration \(a_1\) for a time interval \(t_1\) and with uniform acceleration \(a_2\) for time interval \(t_2\), then the average acceleration $$ a=\frac{a_1t_1+a_2t_2}{t_1+t_2} $$
• A body thrown upwards takes same time for going up (till its velocity becomes zero) as it takes to come down and comes back with the same velocity with which it was throw upward.
• When a body is dropped freely from the top of building and another body is projected horizontally from the same point, both will reach the ground at the same time.
• Time taken to reach earth by a freely falling body from the same height is independent of mass (neglecting air effects).
• For a body projected upwards, the magnitude of velocity at any point in its path is same whether the body is moving upwards or downwards.

Equations of Motion

\[ v_f = v_i+at\qquad \text{or} \qquad v_f=v_i+gt \]

\[ S=v_it+\frac{1}{2}at^2\qquad \text{or} \qquad S=v_it+\frac{1}{2}gt^2 \]

\[ v_f^2=v_i^2+2aS\qquad \text{or} \qquad v_f^2=v_i^2+2gS \]

• Distance traveled in nth second with constant acceleration is $$ S_n=v_i + \frac{1}{2}(2n-1) $$

Newtons Laws of Motion

• Newton's work on physics in his book named PRINCIPIA of mathematics.
• Newton's laws applicable for moving objects having speed not comparable to the speed of light

1^st law (law of inertia)

Every body continues to he in state of rest uniform motion along a straight line unless it is compelled to change that state by an applied

• This law qualitatively defines the force
• The inability of the body to change its state is called inertia. So, it is also known as the inertia of Galileo.
• Inertia resists change in the state of motion of the body.

2^nd Law of Motion (Force and Acceleration)

The effect of an applied force on a body is to cause it to accelerate in the direction of the force. The acceleration is directly proportion to the force and is inversely proportional to the mass of the body.

OR

A force \(F\) acting on a body is equal to its change in momentum per second.

To be completed...

F cc Mass of the body x Change in velocity per second ma F k ma (where k is a constant) But k = 1 F = ma Weight: The weight of a body is equal to the force with which the body is attracted b) earth towards its center 1111 Motion and p,

(— - When force acts in direction of velocity

Speed increases and direction of motion remain same 3^rd law: When force acts opposite to direction of velocity

Speed decreases and direction of motion remain same When force acts perpendicular to direction of velocity → Only direction changes and magnitude of velocity remain same When force acts at some angle to the direction of velocity. Both magnitude and direction of velocity changes ['AB = f:11,, or = f't-caction Action and reaction forces never acts on the same body.

To be completed...

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