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(a) v= u+at
(b) s= ut+1/2 at^{2}
(c) v^{2}=u^{2}+2as
Here u is the initial velocity, v is the final velocity, a is the acceleration , s is the displacement travelled by the body and t is the time.
Note: Take ‘+ve’ sign for a when the body accelerates and takes ‘–ve’ sign when the body decelerates.
s_{n}= u + a/2 (2n-1)
(i) Variation of displacement (x), velocity (v) and acceleration (a) with respect to time for different types of motion.
Displacement(x)
Velocity(v)
Acceleration (a)
(a) At rest
(b) Motion with constant velocity
(c) Motion with constant acceleration
(d) Motion with constant deceleration
Scalar Quantities:- Scalar quantities are those quantities which require only magnitude for their complete specification.(e.g-mass, length, volume, density)
Vector Quantities:- Vector quantities are those quantities which require magnitude as well as direction for their complete specification. (e.g-displacement, velocity, acceleration, force)
Null Vector (Zero Vectors):- It is a vector having zero magnitude and an arbitrary direction.
When a null vector is added or subtracted from a given vector the resultant vector is same as the given vector.
Dot product of a null vector with any arbitrary is always zero. Cross product of a null vector with any other vector is also a null vector.
Parallel vector (θ=0°):- Two vectors acting along same direction are called parallel vectors.
Anti parallel vector (θ=180°):-Two vectors which are directed in opposite directions are called anti-parallel vectors.
Co-planar vectors- Vectors situated in one plane, irrespective of their directions, are known as co-planar vectors.
Vector addition:-
Vector addition is commutative-
Vector addition is associative-
Vector addition is distributive-
Magnitude of resultant vector :-
R=√(A^{2}+B^{2}+2ABcosθ)
Here θ is the angle between and .
If β is the angle between and ,
then,
So,
R=√(A^{2}+B^{2}+2ABcosθ),
Cases 1:- When, θ=0°, then,
R= A+B (maximum), β=0°
Cases 2:- When, θ=180°, then,
R= A-B (minimum), β=0°
Cases 3:- When, θ=90°, then,
R=√(A^{2}+B^{2}), β = tan^{-1} (B/A)
Resolution of vector in a plane:-
(a) Dot product or scalar product:-
,
Here A is the magnitude of , B is the magnitude of and θ is the angle between and .
(i) Perpendicular vector:-
(ii) Collinear vector:-
When, Parallel vector (θ=0°),
When, Anti parallel vector (θ=180°),
(b) Cross product or Vector product:-
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