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Motion: Key Concepts, Formulas, and Practice Questions

This lecture covers the physics topic of motion, explaining relativity of rest and motion, distance, displacement, speed, velocity, acceleration, retardation, equations of motion, projectile motion, circular motion, and Newton's laws. It also solves numerical examples and discusses multiple-choice practice questions aligned with teaching exam syllabi.

Teaching
Physics
English · 7 topics
Checked against the video on 25 Oct 2026

Made by AI from the YouTube video UP SUPERTET SCIENCE Class-3 | गति | TOPIC WISE VIDEO & MCQ PRACTICE | उ प्र प्राथमिक शिक्षक भर्ती (opens YouTube in a new tab) by Balaji Study Adda, then checked against it. All credit for the teaching goes to the creator. Tap a topic’s time to confirm a fact in the video.

Motion: Key Concepts, Formulas, and Practice Questions

English7 topics · 7 MCQs · 10 flashcardsWatch the video (opens YouTube in a new tab)

Checked against the video

In short

This lecture covers the physics topic of motion, explaining relativity of rest and motion, distance, displacement, speed, velocity, acceleration, retardation, equations of motion, projectile motion, circular motion, and Newton's laws. It also solves numerical examples and discusses multiple-choice practice questions aligned with teaching exam syllabi.

Relativity of Rest and Motion, Distance, and Displacement

Rest describes an object whose position does not change over time relative to its environment, such as a book lying on a table.
Motion describes an object whose position changes over time relative to its surroundings.
Must knowRest and motion are relative terms, meaning a person sitting in a moving train is in motion with respect to someone outside, but at rest with respect to a co-passenger.
Distance is the total path length traversed by an object; it is always a scalar quantity and is always positive.
Must knowDisplacement is the shortest straight-line distance between the initial and final positions of an object; it is a vector quantity that can be positive, negative, or zero.
For a runner completing one full circular lap of radius 14 m, distance equals circumference (2 × (22/7) × 14 = 88 m), while displacement equals 0 because the runner returns to the starting point.

Speed, Velocity, Acceleration, and Retardation

Speed is the distance traveled per unit time, which is a scalar quantity measured in m/s.
Velocity is the displacement per unit time, which is a vector quantity measured in m/s.
Must knowAcceleration is defined as the rate of change of velocity, measured in m/s².
Retardation is negative acceleration occurring when velocity decreases with time.

Equations of Motion with Solved Numerical Problems

Motion in a straight line under uniform acceleration is governed by three primary equations: v = u + at, s = ut + (1/2)at², and v² = u² + 2as.
A car starting from rest (u = 0) accelerating at 4 m/s² for 5 seconds reaches a final velocity of 20 m/s using v = u + at (0 + 4 × 5 = 20 m/s).
The distance covered by that car in 5 seconds is calculated using s = ut + (1/2)at², giving s = 0 + (1/2)(4)(5²) = 50 m.
Must knowWhen a vehicle moving at 20 m/s applies brakes producing a retardation of 10 m/s², acceleration is substituted as negative (a = -10 m/s²), bringing final velocity v to 0.
Using v² = u² + 2as with u = 20, v = 0, and a = -10: 0 = 400 + 2(-10)s yields a stopping distance s = 20 m.

Projectile Motion

Projectile motion is 2D motion where an object thrown into the air at an angle θ to the horizontal traces a parabolic path, such as a thrown javelin or a fired cannonball.
Time of flight (T) is the total time spent in the air, calculated as T = (2u sin θ) / g.
Maximum height (H) reached above the ground is given by H = (u² sin² θ) / (2g).
Horizontal range (R) is the total horizontal distance covered before landing, calculated as R = (u² sin 2θ) / g.
Must knowAn object achieves maximum range when launched at an angle of 45 degrees because sin(2 × 45°) = sin(90°) = 1, which is the maximum possible value for sine.
Two projectiles launched at the same initial speed at complementary angles θ and (90° - θ), such as 30° and 60°, achieve the exact same horizontal range.

Circular Motion and Forces

Centripetal force acts towards the center along the circular path to maintain circular motion, expressed by the formula F = (mv²) / r.
The gravitational pull between the Sun and Earth acts as the centripetal force keeping Earth in orbit.
Must knowCentrifugal force is a pseudo force directed radially outward from the center of a circular path.
Practical devices based on centrifugal force include washing machine dryers and cream separators used to extract butter from milk.

Newton's Laws of Motion and Key Physics Facts

Newton's first law, also known as the Law of Inertia, states that an object opposes any change in its state; examples include dust falling off a beaten carpet and passengers falling forward when a bus suddenly stops.
Newton's second law is the law of momentum, stating that Force equals mass times acceleration (F = ma); an example is a cricket player pulling hands backward while catching a fast ball.
Newton's third law is the action-reaction law, stating that every action has an equal and opposite reaction; examples include rocket propulsion and the recoil of a gun.
An odometer measures the total distance traveled by a vehicle, while a speedometer measures its instantaneous speed.
Galileo first proposed the concept of inertia; heavier objects have greater inertia.
The acceleration due to gravity (g) is maximum at the poles, which makes the weight of an object greatest at the poles.

Practice MCQs on Motion and Mechanics

A bicycle wheel moving forward on a straight road exhibits both circular (rotational) and translational motion.
When distance covered in a circular path is directly proportional to time, speed remains constant, but velocity continuously changes due to constant change in direction.
In uniform circular motion, speed remains constant, whereas velocity and acceleration continuously change direction.
A body dropped freely from height h reaches ground with final velocity v = √(2gh); with g = 10 m/s², v = √(20h) m/s.
The mass of an object remains constant under all conditions, whereas weight can change depending on gravitational acceleration.
If Earth's rotational speed increases, centrifugal force increases, reducing effective gravitational acceleration (g) and causing body weight to decrease.
When an object is taken to the Moon, its weight decreases because lunar gravity is 1/6th of Earth's gravity, while its mass remains unchanged.
The opposing force that stops a vehicle when brakes are applied is frictional force between the tires and road surface.

Quantity	Type	SI Unit	Formula / Nature
Distance	Scalar	m	Always positive
Displacement	Vector	m	Positive, negative, or zero
Speed	Scalar	m/s	Distance / Time
Velocity	Vector	m/s	Displacement / Time
Acceleration	Vector	m/s²	Change in Velocity / Time
Force	Vector	N (kg·m/s²)	F = ma

Key terms

Inertia: The inherent tendency of an object to resist any change in its state of rest or uniform motion.
Retardation: Negative acceleration occurring when the velocity of an object decreases over time.
Centripetal Force: The center-directed force required to keep an object moving along a curved circular path.
Centrifugal Force: An apparent pseudo-force directed away from the center in a rotating circular frame of reference.
Momentum: The product of mass and velocity of a moving object (p = mv).

Formulas

v = u + at: First equation of linear motion
s = ut + (1/2)at²: Second equation of linear motion (calculating distance/displacement)
v² = u² + 2as: Third equation of linear motion relating velocity, acceleration, and distance
T = (2u sin θ) / g: Time of flight for a projectile
H = (u² sin² θ) / (2g): Maximum height reached by a projectile
R = (u² sin 2θ) / g: Horizontal range of a projectile
F = (m × v²) / r: Centripetal force formula
F = m × a: Newton's second law of motion (Force)
W = m × g: Weight of an object

Exam tips and traps

Always assign a negative sign to acceleration when retardation occurs or when brakes are applied to an initially moving object.
In projectile motion, launch angles θ and (90° - θ) produce identical horizontal ranges when initial velocity is constant.

Quick revision

Read these the night before the exam.

Distance is a scalar quantity and is always positive, while displacement is a vector quantity that can be zero.
The SI unit of acceleration is m/s², and negative acceleration is known as retardation.
For maximum horizontal range in projectile motion, the angle of projection must be 45 degrees.
Complementary launch angles such as 30 degrees and 60 degrees yield identical horizontal ranges.
Cream extraction from milk and washing machine dryers work on the principle of centrifugal force.
Newton's first law of motion is also called the Law of Inertia, first stated by Galileo.
Rocket propulsion and gun recoil operate on Newton's third law of motion (action-reaction).
An odometer measures total distance traveled, while a speedometer measures instantaneous speed.
Acceleration due to gravity (g) and body weight are maximum at the Earth's poles.
Mass remains constant everywhere, while weight on the Moon is 1/6th of weight on Earth.

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