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GENERAL SCIENCE · CLASS 8–10 SERIES

Motion, Force, Newton's Laws and Gravitation

Distance and displacement, speed, velocity and acceleration, Newton's three laws with everyday examples, momentum, free fall, g, and mass versus weight.

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Oil painting of Isaac Newton as a man of about 46, with long grey hair and a dark coat
Isaac Newton (1642–1727), painted by Godfrey Kneller in 1689. In 1687 his book Principia gave the three laws of motion and the law of gravitation. The SI unit of force, the newton (N), is named after him. Image: Godfrey Kneller, Wikimedia Commons · Public domain

Why do bus passengers fall forward when the driver brakes? How does a rocket rise? Why does a ball thrown up always come down? Three laws of motion and one law of gravitation answer all of these. This page starts from distance and speed, then builds up Newton's laws, momentum, free fall and weight.

On this page you will learn:

  • Distance and displacement; speed, velocity and acceleration
  • Force, inertia and Newton's three laws
  • Momentum, recoil of a gun and how a rocket works
  • Gravitation, free fall, g, and mass versus weight
9.8 m/s²
g on Earth
Same for every falling body
1/6
Weight on the Moon
Compared with Earth
0
Weight at Earth's centre
Because g = 0 there

Describing motion

Rule in one line: distance is the path covered; displacement is the straight line from start to finish.

SCALARS VS VECTORS
Scalar
Vector
Has
Size only
Size and direction
Examples
Distance, speed, mass
Displacement, velocity, force
After one full round
Distance: not zero
Displacement: zero
A runner who finishes one round of a 400 m track covers 400 m of distance, but the displacement is zero.
QuantityMeaningSI unit
SpeedDistance ÷ timem/s
VelocityDisplacement ÷ time (speed with direction)m/s
AccelerationChange in velocity ÷ timem/s²
RetardationNegative acceleration: the body slows downm/s²
To turn km/h into m/s, multiply by 5/18. So 36 km/h = 10 m/s and 72 km/h = 20 m/s.
EquationLinks
v = u + atVelocity and time
s = ut + ½at²Distance and time
v² − u² = 2asDistance and velocity
The three equations of motion, for uniform acceleration. u = starting velocity, v = final velocity, a = acceleration, t = time, s = distance.
KEY TERM
Uniform circular motion

A body moving in a circle at constant speed keeps changing direction. So its velocity changes, and the motion is accelerated. The force that keeps it on the circle points to the centre. It is called the centripetal force. The Moon going round the Earth is an example.

QUICK FACT

On a distance–time graph, the slope gives the speed. On a velocity–time graph, the slope gives the acceleration and the area under the line gives the distance. A vehicle's odometer records distance; its speedometer shows speed.

Force and Newton's three laws

Rule in one line: first law inertia, second law F = ma, third law action and reaction.

A force is a push or a pull. It can start or stop motion, change speed or direction, or change shape. Its SI unit is the newton (N). 1 N gives a mass of 1 kg an acceleration of 1 m/s². Only an unbalanced force changes motion. In a tug of war where nobody moves, the forces are balanced.

CONTACT FORCES
  • Muscular force: lifting a bucket
  • Friction: a rolling ball slowly stops
NON-CONTACT FORCES
  • Magnetic force: a magnet pulls iron pins
  • Electrostatic force: a rubbed comb pulls paper bits
  • Gravity: fruit falls from a tree
LawWhat it saysEveryday examples
First law (law of inertia)A body stays at rest, or keeps moving in a straight line, until an unbalanced force acts on itPassengers fall forward when a bus stops suddenly; dust leaves a beaten carpet
Second lawForce = rate of change of momentum, so F = maA fielder pulls the hands back while catching; high jumpers land on soft mats
Third lawEvery action has an equal and opposite reaction, acting on a different bodyRecoil of a gun; a rocket rising; a swimmer pushing water back
Pulling the hands back gives the ball more time to stop. More time means less force on the hands.
KEY TERM
Inertia

Inertia is a body's tendency to resist any change in its rest or motion. Mass is the measure of inertia: a loaded truck is harder to start or stop than a bicycle. When a bus starts suddenly, standing passengers fall backward (inertia of rest). When it stops suddenly, they fall forward (inertia of motion).

Bus stops→Feet stop with it→Upper body keeps moving→We fall forward
KEY TERM
Momentum

Momentum (p) = mass × velocity. Its unit is kg m/s. If no outside force acts, the total momentum stays the same: the law of conservation of momentum. When a gun fires, the bullet goes forward and the gun moves back with equal and opposite momentum. This backward kick is the recoil.

p = m × v
Computer-made picture of five shiny steel balls hanging in a row from thin strings on a frame, resting on an old book
Newton's cradle, standing on a copy of Newton's Principia. Lift one end ball and let it hit the row: one ball flies out at the other end. Momentum passes through the row and is conserved. Image: DemonDeLuxe (Dominique Toussaint), Wikimedia Commons · CC BY-SA 3.0
A tall white rocket lifting off its launch tower, with a huge burst of flame and smoke below it
The Saturn V rocket of Apollo 11 lifts off, 16 July 1969. Hot gases rush down (action); the gases push the rocket up (reaction). This is Newton's third law, and also conservation of momentum. Image: NASA, Wikimedia Commons · Public domain
QUICK CHECK
PYQ · PPSC TM 2015 — The working of a rocket is based on the principle postulated by:
Tap an option to answer

Gravitation, free fall and weight

Rule in one line: a falling body gains speed, but its acceleration g stays the same.

KEY TERM
Universal law of gravitation

Every two objects in the universe pull each other. The force grows with their masses and falls with the square of the distance between them: F = G m₁m₂ / d². Double the distance, and the force becomes one-fourth. G is the universal gravitational constant, 6.67 × 10⁻¹¹ N m²/kg², the same everywhere.

  • It makes objects fall and holds us to the Earth
  • It keeps the Moon going round the Earth, and the planets round the Sun
  • The Moon's pull causes tides in the sea
A STONE IN FREE FALL (NO AIR RESISTANCE)
  1. 1
    0 s: dropped
    Speed 0 m/s
  2. 2
    After 1 s
    Speed about 9.8 m/s
  3. 3
    After 2 s
    Speed about 19.6 m/s
  4. 4
    After 3 s
    Speed about 29.4 m/s
Speed and velocity grow by 9.8 m/s every second (v = gt). The acceleration — the amount added each second — is constant.
KEY TERM
Acceleration due to gravity (g)

Near the Earth's surface every freely falling body speeds up at about 9.8 m/s², whatever its mass. In a vacuum a feather and a coin fall together. g is a little more at the poles than at the equator. It falls as we go up, and also as we go down into the Earth. At the centre of the Earth, g is zero.

QUICK CHECK
PYQ · PPSC DDSWO 2026 — Which is constant for a freely falling object?
Tap an option to answer
QUICK CHECK
PYQ · PPSC TM 2015 — A body falling freely from a height towards the earth moves with uniform:
Tap an option to answer
MASS VS WEIGHT
Mass
Weight
What it is
Amount of matter
Pull of gravity on it
Formula
m
W = m × g
SI unit
kilogram (kg)
newton (N)
On the Moon
Same
About 1/6
At Earth's centre
Same
Zero
Measured with
Beam balance
Spring balance
Weight is a force, so it is measured in newtons, not kilograms.
Value of g at different places
Earth's poles
9.83
Earth's equator
9.78
Moon
1.62
Earth's centre
0
Weight = m × g, so weight follows g. It is least at the centre of the Earth, where it is zero.
An astronaut in a white spacesuit with a gold visor standing on the grey, dusty surface of the Moon
Buzz Aldrin on the Moon, Apollo 11, 1969. The Moon's g is about one-sixth of the Earth's. So his heavy suit weighed only about one-sixth as much, though its mass was the same. Image: Neil Armstrong (NASA), Wikimedia Commons · Public domain
QUICK CHECK
PYQ · PSCB Manager — Where will the weight of an object be least?
Tap an option to answer
An astronaut inside the space station watching a round ball of liquid floating in the air in front of his face
NASA astronaut Jack Fischer on the International Space Station watches his drink float as a ball. Gravity is still there; the station and everything in it are falling freely round the Earth together. So they feel weightless. Image: NASA, Wikimedia Commons · Public domain
More facts asked once in a whileTap to open
  • Escape velocity from the Earth is about 11.2 km/s: the least speed a body needs to leave the Earth's pull without more push.
  • Galileo showed that, without air, heavy and light bodies fall at the same rate.
  • Kepler's laws describe how planets move round the Sun in elliptical orbits. Newton's law of gravitation explains them.
  • Action and reaction act on different bodies, so they never cancel each other.

Traps and practice

Last revision — where the options try to fool you.

COMMON TRAPS
  • Free fall: acceleration is constant; velocity and speed are not.
  • g (9.8 m/s², changes from place to place) is not G (6.67 × 10⁻¹¹ N m²/kg², same everywhere).
  • Least weight: the centre of the Earth (zero). On the surface: the equator.
  • Rocket and gun recoil: Newton's third law — not Kepler, not Einstein.
  • Bus starts: fall backward (inertia of rest). Bus stops: fall forward (inertia of motion).
  • Uniform circular motion is accelerated motion, though the speed is constant.
CHECK YOURSELF

A car starts from rest and reaches 20 m/s in 5 s. What is its acceleration?

Show answer

a = (v − u) / t = (20 − 0) / 5 = 4 m/s².

CHECK YOURSELF

A person has a mass of 60 kg. What is the weight on Earth (g = 10 m/s²) and on the Moon?

Show answer

On Earth W = 60 × 10 = 600 N. On the Moon it is about one-sixth: 100 N. The mass stays 60 kg in both places.

FLASHCARDS
Motion and gravitation flashcards
SI unit of force
Newton (N)
Measure of inertia
Mass
Momentum
Mass × velocity
How a rocket works
Newton's third law
Constant in free fall
Acceleration (g)
g on Earth
9.8 m/s²
Least weight
Centre of the Earth
36 km/h in m/s
10 m/s
QUICK BYTES
  • Distance scalar; displacement vector
  • km/h × 5/18 = m/s
  • v = u + at; s = ut + ½at²; v² − u² = 2as
  • First law inertia; second F = ma; third action–reaction
  • p = mv; momentum is conserved; rocket and recoil
  • g = 9.8 m/s²; more at poles; zero at Earth's centre
  • Weight = mg, in newtons; Moon weight about 1/6

Frequently Asked Questions

What is the difference between distance and displacement?

Distance is the whole length of the path and has no direction. Displacement is the straight-line gap from start to finish, with direction. After a full round, displacement is zero.

What are Newton's three laws of motion?

First: a body stays at rest or in uniform motion until an unbalanced force acts (inertia). Second: F = ma. Third: every action has an equal and opposite reaction.

Which law explains how a rocket works?

Newton's third law. Gases are pushed out downward and they push the rocket upward. It is also conservation of momentum.

Why do passengers fall forward when a bus stops suddenly?

Because of inertia of motion. The feet stop with the bus, but the upper body tends to keep moving forward.

What is momentum?

Momentum is mass times velocity, p = mv, in kg m/s. Without an outside force the total momentum stays the same. That is why a gun recoils.

What stays constant for a freely falling body?

Its acceleration, g, about 9.8 m/s². Its speed and velocity keep increasing as it falls.

What is the value of g?

About 9.8 m/s² near the Earth's surface. It is a little more at the poles than at the equator. It falls with height and with depth, and is zero at the Earth's centre.

Where is the weight of a body least?

At the centre of the Earth, where g and so weight are zero. On the surface, weight is less at the equator than at the poles.

What is the difference between mass and weight?

Mass is the amount of matter, in kilograms, and is the same everywhere. Weight is the pull of gravity, W = mg, in newtons, and it changes from place to place.

Why do astronauts float in a space station?

Gravity still acts on them. They and the station fall freely round the Earth together, so they feel weightless.

Now sit the questions they actually set

Previous-year PPSC questions on this topic, free to read with the worked answer.

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