CLASS XI | PHYSICS | CHAPTER 3
notes prepared by subhankar Karmakar
Rest : An object is said to be at rest if it does not change its position with respect to its surroundings with time.
Motion: An object is said to be in motion if it changes its position with respect to its surroundings with time.
Distance / path length: (s or x)
It is the length of the actual path travelled by a body between its initial and final positions. It is a scalar quantity.
The SI unit of distance is metre
The CGS unit of distance is centimetre
Displacement: (s or x)
The displacement of an object is the change in the position of an object in a fix direction. It is a vector quantity.
The SI unit of displacement is metre
The CGS unit of displacement is centimetre
Speed: (v)
The distance travelled per unit time is called speed.
Speed = distance travelled/ time taken
v = s/t
It is a scalar quantity
The SI unit of speed is m/s or ms⁻¹
The CGS unit of speed is cm/s or cms⁻¹
The dimensional formula of speed is [M⁰L¹T⁻¹]
Velocity: (v)
The rate of change of position of an object which time in a given direction is called its velocity.(v)
Velocity= displacement/time
It is a vector quantity.
SI unit of velocity is m/s
CGS unit of velocity is cm/s
The dimensional formula of velocity is [M⁰L¹T⁻¹]
Acceleration:
The rate of change of velocity of an object with time is called its acceleration. (a)
Acceleration= change in velocity/time taken
It is a vector quantity.
The SI unit of acceleration is m/s²
The CGS unit of acceleration is cm/s²
The dimensional formula of acceleration is [M⁰L¹T⁻²]
Different types of speed
There are four types of speed
1. Uniform speed
2. Variable speed
3. Average speed
4. Instantaneous speed
Uniform speed: if a body covers equal distances in equal intervals of time the body is said to be in uniform speed.
Variable speed: if a body covers unequal distances in equal intervals of time the body is in variable speed.
Average speed: the ratio of Total distance travelled and total time taken is called average speed
Instantaneous speed: the speed of an object at any particular instant of time is called instantaneous speed of that object.
Different types of velocity:
There are basically four types of velocity
1. Uniform velocity
2. Variable velocity
3. Average velocity
4. Instantaneous velocity
Uniform velocity: a body is said to be moving with uniform velocity if it covers equal displacements in equal intervals of time.
Variable velocity: a body is said to be moving with variable velocity if either its speed changes or direction of motion changes or or both change with time
Average velocity: the ratio of total displacement and total time is called average velocity
Instantaneous velocity: the velocity of an object at a particular instant of time or at a particular point of its path is called its instantaneous velocity.
How to calculate average speed in different situations:
a. A body covering different distances with different speeds:
Suppose a body covers distances s₁, s₂, s₃.... with speeds v₁, v₂, v₃... respectively, then its average speed will be
vₐ = (s₁+ s₂ + s₃... )/(t₁ + t₂ + t₃... )
⟹ vₐ = (s₁+ s₂ + s₃... )/(s₁/v₁ + s₂/v₂ + s₃/v₃ .....)
(i) if s₁ = s₂ = s
vₐ = (s₁+ s₂)/(s₁/v₁ + s₂/v₂)
⟹ vₐ = (s + s)/(s/v₁ + s/v₂)
⟹ vₐ = (2s)/s(1/v₁ + 1/v₂)
⟹ vₐ = (2v₁v₂)/(v₁ + v₂)
As an example suppose a body travels from A to B at 40 m/s and from B to A at 60 m/s. Calculate the average speed.
Soln. Here the distances of same ie. s₁ = s₂ = s
As AB distance = BA distance
∴ vₐ = (2v₁v₂)/(v₁ + v₂)
⟹ vₐ = (2x40x60)/(40 + 60)
⟹ vₐ = (2x40x60)/100
⟹ vₐ = 48 m/s
b. A body moving with different speeds in different time intervals:
Suppose a body travels with speeds v₁, v₂, v₃, ...
In time intervals t₁, t₂, t₃ .......
Respectively, then
Total distance travelled = v₁t₁ + v₂t₂ + v₃t₃ + .....
Total time taken = t₁ + t₂ + t₃ + ........
∴ vₐ = (v₁t₁ + v₂t₂ + v₃t₃ + .....)/( t₁ + t₂ + t₃ + ..)
As an example, if a body travels along a straight line for the first 10 minutes with speed 30 km/h, and the next 20 minutes with speed 60 km/h. Find the average speed of the body.
Soln. Here, v₁ = 30 km/h; v₂ = 60 km /h
t₁ = 10 min = 10/60 h = 1/6 h
t₂ = 20 min = 20/60 h = 2/6 h
∴ t₁ + t₂ = 1/6 + 2/6 = 3/6 = 1/2 h
We know, vₐ = (v₁t₁ + v₂t₂)/( t₁ + t₂)
∴ vₐ = {30x(1/6)+60x(2/6)}/(1/2)
⟹ vₐ = (5 + 20)/(1/2)
⟹ vₐ = 25x2 = 50 km/h
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