Motion
Introduction
Motion is everywhere around us. Birds flying, water flowing in rivers, cars moving on roads, planets revolving around the sun - all these are examples of motion. Motion is one of the most fundamental concepts in physics.
Motion: An object is said to be in motion if it changes its position with respect to its surroundings with time.
Rest and Motion
Rest: An object is said to be at rest if it does not change its position with respect to its surroundings with time.
Important Points:
- Rest and motion are relative terms
- An object may be at rest with respect to one object while in motion with respect to another
- Example: A passenger sitting in a moving train is at rest with respect to the train but in motion with respect to trees outside
Types of Motion
1. Translational Motion: Motion in which all parts of the object move through the same distance in the same time (Example: A car moving on a straight road)
2. Rotational Motion: Motion in which an object rotates about a fixed axis (Example: A spinning top, Earth rotating on its axis)
3. Vibrational Motion: Motion in which an object moves to and fro about a fixed point (Example: Pendulum, vibrating string of a guitar)
Describing Motion
To describe motion, we need to specify:
- Position of the object
- Direction of motion
- Speed or how fast it is moving
Distance and Displacement
Distance: The total path length covered by an object is called distance. It is a scalar quantity (has only magnitude).
Unit: Meter (m) in SI system
Symbol: s or d
Displacement: The shortest distance between the initial and final positions of an object along with direction is called displacement. It is a vector quantity (has both magnitude and direction).
Unit: Meter (m) in SI system
Symbol: s or Δx
Key Differences:
| Distance | Displacement |
|---|---|
| Total path length | Shortest path with direction |
| Scalar quantity | Vector quantity |
| Always positive | Can be positive, negative or zero |
| Distance ≥ Displacement | Magnitude of displacement ≤ Distance |
Speed and Velocity
Speed: The distance traveled by an object per unit time is called speed. It is a scalar quantity.
Speed = Distance / Time
v = s / t
v = s / t
Unit: m/s (meter per second) or km/h
Velocity: The displacement of an object per unit time is called velocity. It is a vector quantity.
Velocity = Displacement / Time
v = s / t
v = s / t
Unit: m/s (meter per second)
Types of Speed:
- Uniform Speed: When an object covers equal distances in equal intervals of time
- Non-uniform/Variable Speed: When an object covers unequal distances in equal intervals of time
- Average Speed: Total distance traveled / Total time taken
- Instantaneous Speed: Speed at a particular instant of time
Acceleration
Acceleration: The rate of change of velocity is called acceleration. It is a vector quantity.
Acceleration = Change in Velocity / Time
a = (v - u) / t
Where:
a = acceleration
v = final velocity
u = initial velocity
t = time
a = (v - u) / t
Where:
a = acceleration
v = final velocity
u = initial velocity
t = time
Unit: m/s² (meter per second square)
Types of Acceleration:
- Positive Acceleration: When velocity increases with time (a > 0)
- Negative Acceleration (Retardation/Deceleration): When velocity decreases with time (a < 0)
- Zero Acceleration: When velocity remains constant (a = 0)
- Uniform Acceleration: When velocity changes by equal amounts in equal intervals of time
- Non-uniform Acceleration: When velocity changes by unequal amounts in equal intervals of time
Equations of Motion (Kinematic Equations)
For objects moving with uniform acceleration, we have three equations of motion:
First Equation of Motion:
v = u + at
Second Equation of Motion:
s = ut + ½at²
Third Equation of Motion:
v² = u² + 2as
Where:
u = initial velocity
v = final velocity
a = acceleration
t = time
s = displacement
v = u + at
Second Equation of Motion:
s = ut + ½at²
Third Equation of Motion:
v² = u² + 2as
Where:
u = initial velocity
v = final velocity
a = acceleration
t = time
s = displacement
Derivation of Equations of Motion
First Equation: v = u + at
We know that:
Acceleration = Change in velocity / Time
a = (v - u) / t
at = v - u
v = u + at
Acceleration = Change in velocity / Time
a = (v - u) / t
at = v - u
v = u + at
Second Equation: s = ut + ½at²
Average velocity = (u + v) / 2
Distance = Average velocity × Time
s = [(u + v) / 2] × t
From first equation: v = u + at
s = [(u + u + at) / 2] × t
s = [(2u + at) / 2] × t
s = ut + ½at²
Distance = Average velocity × Time
s = [(u + v) / 2] × t
From first equation: v = u + at
s = [(u + u + at) / 2] × t
s = [(2u + at) / 2] × t
s = ut + ½at²
Third Equation: v² = u² + 2as
From first equation: v = u + at, so t = (v - u) / a
From second equation: s = ut + ½at²
s = u[(v - u) / a] + ½a[(v - u) / a]²
s = [u(v - u) / a] + [a(v - u)² / 2a²]
s = [u(v - u) / a] + [(v - u)² / 2a]
2as = 2u(v - u) + (v - u)²
2as = 2uv - 2u² + v² - 2uv + u²
2as = v² - u²
v² = u² + 2as
From second equation: s = ut + ½at²
s = u[(v - u) / a] + ½a[(v - u) / a]²
s = [u(v - u) / a] + [a(v - u)² / 2a²]
s = [u(v - u) / a] + [(v - u)² / 2a]
2as = 2u(v - u) + (v - u)²
2as = 2uv - 2u² + v² - 2uv + u²
2as = v² - u²
v² = u² + 2as
Graphical Representation of Motion
1. Distance-Time Graph:
- Shows how distance changes with time
- Slope of distance-time graph = Speed
- Straight line with positive slope = Uniform motion
- Curved line = Non-uniform motion
- Steeper the slope, greater the speed
- Horizontal line = Object at rest
2. Velocity-Time Graph:
- Shows how velocity changes with time
- Slope of velocity-time graph = Acceleration
- Horizontal line = Uniform velocity (zero acceleration)
- Straight line with positive slope = Uniform acceleration
- Straight line with negative slope = Uniform retardation
- Area under velocity-time graph = Displacement
Uniform Circular Motion
Uniform Circular Motion: When an object moves along a circular path with constant speed, its motion is called uniform circular motion.
Key Points:
- Speed remains constant but velocity changes (direction changes)
- Acceleration is always directed towards the center (centripetal acceleration)
- Examples: Motion of planets around the sun, motion of moon around Earth, tip of second hand of a clock
Important Formulas Summary
Speed and Velocity:
Speed = Distance / Time
Velocity = Displacement / Time
Average Speed = Total Distance / Total Time
Average Velocity = Total Displacement / Total Time
Acceleration:
a = (v - u) / t
Equations of Motion:
v = u + at
s = ut + ½at²
v² = u² + 2as
Conversion:
1 km/h = 5/18 m/s
1 m/s = 18/5 km/h = 3.6 km/h
Speed = Distance / Time
Velocity = Displacement / Time
Average Speed = Total Distance / Total Time
Average Velocity = Total Displacement / Total Time
Acceleration:
a = (v - u) / t
Equations of Motion:
v = u + at
s = ut + ½at²
v² = u² + 2as
Conversion:
1 km/h = 5/18 m/s
1 m/s = 18/5 km/h = 3.6 km/h
Important Points to Remember
- Motion is relative - depends on the observer
- Distance is always greater than or equal to displacement
- Speed is always positive; velocity can be positive or negative
- Acceleration can be positive, negative, or zero
- In uniform motion: distance = displacement, speed = velocity
- For objects thrown vertically upward: a = -g = -9.8 m/s²
- At highest point of vertical motion: v = 0, but a ≠ 0 (a = -g)
- In uniform circular motion: speed is constant but velocity changes
- Slope of distance-time graph gives speed
- Slope of velocity-time graph gives acceleration
- Area under velocity-time graph gives displacement
Multiple Choice Questions (MCQ)
Subjective Questions
Practice these questions to strengthen your understanding. Write your answers in the space provided.