CLASS 11 MOTION IN STRAIGHT LINE
MOTION IN A STRAIGHT LINE
* Point of reference:
→ It is a virtual point with regard to describe the position of an object.
* Frame of reference:
→ It is a collection of point of reference.
* Distance:-
→ It is the length of actual path, b/w initial & final position
→ It is a scalar quantity
→ It can't be negative.
* Displacement:
→ It is defined as the shortest distance b/w initial & final position of a body.
→ It is vector quantity
→ It may be +ve, -ve or zero.
* Positive displacement:-
→ If direction of motion & displacement are same
* Zero displacement :
→ When initial & final point coincide each other then it is called zero displacement
* DISTANCE => DISPLACEMENT
Distance = Displacement when motion is in a straight line.
* Speed:-
→ It is defined as the rate of change of distance [ speed = distance / time ]
→ S.I unit is m/s → MLT⁻¹
→ It is a scalar quantity → It can't be negative.
* Average speed :-
→ It is defined as the total distance covered by a body in given time.
S_avg= (d_1+ d_2+ ......)/(t_1+ t_2+ ........)
* Velocity :-
→ It is defined as the rate of change of displacement.
[ V = Displacement / time ]
V = (ds)/t Slunit : m/s
M°LT-1
→ It may bee +ve,-ve or zero.
→ Directional speed is called Velocity.
* Instantaneous Velocity:-
→ It is the velocity(speed) of a body at any particular time.
∴ V ⃗ = lim┬(t→0)〖(du )/dt〗
* Average Velocity :-
→ Let initial velocity of a body is u & final velocity v & final
✥ Avg velocity = u+v / 2
NOTE:
V = BC / AC
V= tanθ
* Acceleration:-
→ It is defined as the rate of change of Velocity.
Acc. = Change in Velocity / time Slunit: m/s², LT-2
a = (v – u) / t or a = dv / dt
* Zero Acceleration :-
→ If velocity of a lady doesn't change with time
* Negative Acceleration
→ When breaks .etc are applied on a moving object then it is called negative acceleration.
EQUATIONS OF MOTION
1) FIRST EQUATION OF MOTION
→ we know
a = dv/dt
adt = dv
=> dv = adt
Integrate both side
∫dv = ∫adt
(V)vu = a(t)t0
(v - u) = a(t - 0)
v-u = at
v = u + at
2) SECOND EQUATION OF MOTION
→ we know
v = dx/dt
vdt = dx
dx = vdt
Integrate both sides
∫dx = ∫vdt = ∫0t (uiat)dt
∫dx = ∫0t udt + ∫0t at'dt
(x)s0 = u(t)t0 + a (t2/2)t0
S-0 = u(t-0) + 1/2a(t2-0)
S = ut + 1/2at2
3) THIRD EQUATION OF MOTION
→ we know
a = (dv/dx) * (du/dt)
a = dv/dx * v
a dx = vdv
v dv = a dx
∫v dv = a∫dx
(v2/2)vu = a(x)s0
1/2(v2-u2) = a(s-0)
v2-u2 = 2as
v2 = u2+2as
Distance in nth second :
We know distance in n seconds,
Sn = u + 1/2 an² --------- ①
Distance in (n-1)th second :
S(n-1) = u(n-1) + 1/2 a(n-1)²
Sn - Sn-1 = un +1/2 an2 - u(n-1) - 1/2 a(n-1)²
= un - un + u + 1/2 an² - 1/2 a(n² - n²)
= u + 1/2 a [n² - n²-1 + 2n]
Dn = u + 1/2 a [2n-1]
* Some formulas:
In Retardation
① v = u-at
② S = ut - 1/2 at²
③ v² = u² - 2as
At Max height
v = 0
In freefall
u = 0
In Dropping ball
u = 0
* RELATIVE SPEED
Cos α = BC / v2
BC = v2 x cos α
In ∆ACO, By PGT
AD² = AC² + CD²
= (V₁ + V₂cosα)² + (V₂ sinα)²
= V₁² + V₂²cos²α + 2V₁V₂cosα + V₂²sin²α
V² = (V₁)² + (V₂)² + 2V₁V₂ cosα
V² = (V₁)² + (V₂)² + 2V₁V₂ cos(180 - θ)
V = √(V₁² + V₂² - 2V₁V₂ cosθ)
1) If θ = 0°
=> in same direction
V = √(V₁)² + (V₂)² - 2V₁V₂
= √(V₁ - V₂)²
V = V₁ - V₂
2) If θ = 180°
=> in op posite direction
V = √(V₁)² + (V₂)² - 2V₁V₂ cos180°
V = √(V₁² + V₂² + 2V₁V₂
V = V₁ + V₂
3) If θ = 90°
V = √(V₁)² + (V₂)² - 2V₁V₂ cos90°
V = √(V₁² + (V₂)²
* * * * * * * * * * * * *
