How Forces Affect Motion Class 9 Notes, Laws of Motion and Numericals

What How Forces Affect Motion is about

Weightage: This chapter is part of Unit III, Motion, Force, Work and Sound, which carries 23 of the 80 theory marks in the school annual exam, shared with Describing Motion Around Us, Work, Energy, and Simple Machines and Sound Waves: Characteristics and Applications.Source: CBSE Science (086) syllabus, Class IX 2026-27, course structure, Unit III Motion, Force, Work and Sound

Key concepts

Force, its measurement, and net force

NCERT section 6.2 Balanced and Unbalanced Forces

A force is a push or pull. It can start motion, stop it, change speed or direction, and change shape (kicking a ball, a bat deflecting a ball, squeezing a lemon). Force needs a magnitude and a direction; change either and its effect changes.

• SI unit: newton (N), written with a small 'n'; symbol capital N.
• A spring balance measures force, not just weight. Holding a 100 g mass needs about 1 N.
• Examples with direction: friction (opposite to motion), gravitational force (towards the Earth), buoyant force (upwards), magnetic and electrostatic forces (attraction or repulsion).

Net force is the single force with the same effect as all the forces together (forces along one line):

• same direction: add the magnitudes;
• opposite directions: subtract, and the net force points along the larger one;
• equal and opposite on one object: net force zero: the forces are balanced.

A tug of war with equal pulls does not move the rope (balanced); if one team pulls harder, the rope moves towards it (unbalanced). The motion of an object depends only on the net force.

Worked example

A box has a 12 N force to the right and a 7 N force to the left acting on it. Find the net force. What if both act to the right? What would make the forces balanced?

Try it first, then show the solutionSolution

1. Opposite directions: $12-7=5$ N to the right.
2. Same direction: $12+7=19$ N to the right.
3. Balanced: the left force must also be 12 N, giving a net force of 0.

Answer: 5 N right; 19 N right; a 12 N force to the left would balance it.

Friction

NCERT section 6.3 The Force of Friction: Often Overlooked but Always Present

Friction acts between surfaces in contact and opposes motion (or the tendency to move).

• A box at rest does not move until your push is larger than the friction; then a net force acts forward.
• Once you stop pushing, friction alone acts backwards, so the box slows down and stops. To keep it moving at constant velocity, you must keep pushing with a force equal to friction.
• Other forces on a pushed box: weight (down) and the normal force from the floor (up, perpendicular to the surface). These two balance.

Activity 6.1: a stack of four coins launched by a stretched rubber band travels further on smoother surfaces (wood < laminate < polished marble). Activity 6.2: pulling a block with a spring balance until it just moves gives the friction; the reading is smallest on the smoothest surface. So friction depends on the nature of the surfaces.

Friction is also useful: we walk by pushing the ground back, and friction pushes us forward. Shoe soles have grooves and tyres have treads to increase it; wet polished floors and icy roads are dangerous because friction is low.

To reduce friction: lubricants, polishing, ball bearings and wheels, streamlined shapes, magnetic levitation.

Worked example

A table is pushed across the floor at constant velocity with a horizontal force of 80 N. What is the friction on it? What happens if the push suddenly drops to 50 N?

Try it first, then show the solutionSolution

1. Constant velocity means zero acceleration, so the net force is zero (first law).
2. So friction $=80$ N, opposite to the push.
3. If the push drops to 50 N, net force $=80-50=30$ N backwards, so the table slows down.

Answer: Friction is 80 N; with a 50 N push the table slows down.

Newton's first law and inertia

NCERT section 6.4 Newton’s First Law of Motion

For centuries people believed a force was needed just to keep something moving. In the 17th century Galileo argued, through thought experiments, that if all obstacles to motion on a level surface were removed, a moving body would keep moving forever. Things normally stop because of friction.

Newton's first law: an object stays at rest, or keeps moving with constant velocity (same speed in the same straight line), unless a net force acts on it.

• If the net force is zero, acceleration is zero.
• Inertia is the tendency of an object to resist any change in its state of rest or uniform motion. The first law is also called the law of inertia. More mass means more inertia.
• Constant velocity does not need a net force; changing velocity (speeding up, slowing down or turning) does.

Graphs with no net force: at rest: position-time is horizontal, velocity-time lies on the time axis. Constant velocity: position-time is a straight sloping line, velocity-time is horizontal.

Everyday inertia: passengers lurch forward when a bus brakes suddenly (their bodies keep moving) and fall back when it starts suddenly; dust leaves a carpet when it is beaten; a coin on a card drops into a glass when the card is flicked away; seat belts stop us continuing forward in a crash.

Worked example

A girl is standing in a bus that brakes suddenly. Explain why she falls forward, and how a seat belt helps a car passenger in a similar situation.

Try it first, then show the solutionSolution

1. Her feet stop with the bus because of friction with the floor.
2. The upper part of her body keeps moving forward because of inertia (first law).
3. A seat belt applies a backward force on the passenger, so the body slows down with the car instead of hitting the dashboard.

Answer: Inertia keeps her upper body moving; a seat belt provides the force needed to stop the passenger safely.

Newton's second law: $F=ma$

NCERT section 6.5 Newton’s Second Law of Motion

Experiments with a cart pulled by a hanging cup (Activities 6.3 and 6.4) show:

• same mass, bigger force → bigger acceleration (a is proportional to F);
• same force, bigger mass → smaller acceleration (a is inversely proportional to m).

In the activity, the cart starts from rest and covers the same distance $s$, so $s=\frac{1}{2}{a}_1{T}_1^2=\frac{1}{2}{a}_2{T}_2^2$, giving $\frac{a_2}{a_1}=\frac{T_1^2}{T_2^2}$. Friction makes the measured ratio a little less than the ideal one.

Newton's second law: when a net force acts on an object, it accelerates in the direction of the net force; the acceleration is proportional to the net force and inversely proportional to the mass:

$a=\frac{F}{m}$, or $F=ma$

One newton is the force that gives a 1 kg mass an acceleration of 1 m s${}^{-2}$: $1\text{ N}=1{\text{ kg m s}}^{-2}$.

Weight: $W=mg$, with $g=9.8$ m s${}^{-2}$ (about 10 for quick estimates). $g$ does not depend on the object's mass.

Momentum $=mv$ (direction of velocity). The fuller form of the law: the rate of change of momentum is proportional to the net force (useful when mass changes, as in rockets).

Worked example

A 1200 kg car goes from rest to 20 m s${}^{-1}$ in 8 s at constant acceleration. Find the net force on it. What net force would give a 600 kg car the same acceleration?

Try it first, then show the solutionSolution

1. $a=\frac{v-u}{t}=\frac{20-0}{8}=2.5$ m s${}^{-2}$.
2. $F=ma=1200\times 2.5=3000$ N in the direction of motion.
3. For 600 kg: $F=600\times 2.5=1500$ N (half the mass needs half the force).

Answer: 3000 N; 1500 N.

Using the second law: stopping forces and safety

NCERT section 6.5 Newton’s Second Law of Motion

From $F=ma$ and $a=\frac{v-u}{t}$: $F=\frac{m(v-u)}{t}$. For the same change in velocity, a longer stopping time means a smaller force.

• Catching a cricket ball: the fielder pulls the hands back, increasing the stopping time, so the ball's deceleration and the force on the hands are smaller, reducing injury.
• Airbags and seat belts: a soft, inflating cushion lengthens the time over which the head and chest stop, so the force is less.
• Packing glass in bubble wrap or hay, landing mats and sand beds in high jump, and bending the knees when jumping down all work the same way.
• Cracking a coconut in one go: it stops in a very short time on a hard surface, so the ground exerts a very large force that breaks the shell.

Combining $F=ma$ with the equations of motion lets you find distances and times: first find $a$ from the net force, then use $v=u+at$, $s=ut+\frac{1}{2}a{t}^2$ or $v^2=u^2+2as$.

Worked example

A 0.15 kg cricket ball moving at 30 m s${}^{-1}$ is caught. Find the average force on the fielder's hands if the ball stops in (i) 0.05 s with stiff hands (ii) 0.3 s when the hands are pulled back.

Try it first, then show the solutionSolution

1. Change in velocity $=0-30=-30$ m s${}^{-1}$.
2. (i) $a=\frac{-30}{0.05}=-600$ m s${}^{-2}$; $F=0.15\times 600=90$ N.
3. (ii) $a=\frac{-30}{0.3}=-100$ m s${}^{-2}$; $F=0.15\times 100=15$ N.
4. Pulling the hands back makes the force six times smaller.

Answer: (i) 90 N (ii) 15 N.

Newton's third law: action and reaction

NCERT section 6.6 Newton’s Third Law of Motion

Forces arise from interaction between two objects. Activity 6.5: sitting on a wheeled chair and pushing a heavy table away moves *you* backwards; pulling the table moves you forwards. Activity 6.6: two spring balances hooked together and pulled always show the same reading.

Newton's third law: whenever one object exerts a force on a second object, the second object at the same time exerts a force of equal magnitude in the opposite direction on the first.

Key points:

• The two forces act on different objects, so they never cancel each other. (Balanced forces act on the same object.)
• Equal forces do not mean equal accelerations, because the masses may differ ($a=\frac{F}{m}$). A falling fruit and the Earth pull each other equally, but the Earth's huge mass gives it a tiny acceleration.
• The law holds for contact and non-contact forces (magnets, charged balloons, gravity).

Examples:

• Walking/cycling off: feet push the ground backwards; friction from the ground pushes you forwards.
• Rowing: paddle pushes water back; water pushes paddle and canoe forward.
• Climbing a coconut tree: legs push down on the trunk; friction pushes the climber up.
• Balloon on a string and rockets: gas is pushed out backwards; the gas pushes the balloon or rocket forwards. Firing an engine ahead slows a spacecraft, as Chandrayaan-3's Vikram lander did before landing.
• Recoil of a gun; a hose pipe pushing back on a fire fighter; a boat moving back when a sailor jumps ashore.

Worked example

A 4 kg gun fires a 20 g bullet, the force on the bullet being 1000 N. Find the initial accelerations of the bullet and the gun.

Try it first, then show the solutionSolution

1. By the third law, the bullet pushes back on the gun with 1000 N.
2. Bullet: $a=\frac{1000}{0.02}=50000$ m s${}^{-2}$ forwards.
3. Gun: $a=\frac{1000}{4}=250$ m s${}^{-2}$ backwards (recoil).
4. Same force, but the much smaller mass of the bullet gives it a much larger acceleration.

Answer: Bullet 50 000 m s${}^{-2}$ forwards; gun 250 m s${}^{-2}$ backwards.

Forces on a system of connected objects

NCERT section 6.7 Forces Acting on a System of Objects

Two boxes of masses $m_1$ and $m_2$ on a smooth floor are joined by a string; a force $F$ pulls Box 1. The string pulls back on Box 1 and forward on Box 2 with a force called tension $T$ (an action-reaction pair through the string).

Treat both boxes and the string as one system:

• Internal forces (the tension) act inside the system and cancel out for the system as a whole.
• Only external forces matter. Vertically, the total weight $(m_1+m_2)g$ is balanced by the normal forces $N_1+N_2$. Horizontally only $F$ acts.

$a=\frac{F}{m_1+m_2}$

The system moves like a single object of mass $m_1+m_2$. Then the tension can be found from the box that only the string pulls: $T=m_{2}a$.

The same idea explains why a tractor pulling a harrow and a trolley together accelerates less than with either alone, and why we can study a walking person as one body even though arms and legs move in complicated ways.

Worked example

Boxes of 3 kg (Box 1, pulled) and 5 kg (Box 2) are tied by a string on a smooth floor. A 16 N force pulls Box 1. Find the acceleration and the tension in the string.

Try it first, then show the solutionSolution

1. $a=\frac{F}{m_1+m_2}=\frac{16}{3+5}=2$ m s${}^{-2}$.
2. Only the string pulls Box 2: $T=m_{2}a=5\times 2=10$ N.
3. Check on Box 1: $F-T=16-10=6$ N $=3\times 2$ ✓.

Answer: 2 m s${}^{-2}$; tension 10 N.

Science in real life: How Forces Affect Motion

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Topics in this chapter

• Net Force, Friction and Newton's First Law
• Newton's Second and Third Laws with Numericals

How Forces Affect Motion: formulas and key facts

Net force (along a line)

Same direction: $F_1+F_2$; opposite directions: $F_1-F_2$ along the larger force.

Second law

$F=ma$, or $a=\frac{F}{m}$

Force from change in velocity

$F=\frac{m(v-u)}{t}$

One newton

$1\text{ N}=1\text{ kg}\times 1{\text{ m s}}^{-2}$

Weight

$W=mg$, $g=9.8{\text{ m s}}^{-2}$ (about 10 for estimates)

Momentum

$p=mv$, in the direction of velocity.

Third law

$F_{AB}=-F_{BA}$: equal size, opposite direction, on different objects.

Connected objects

$a=\frac{F}{m_1+m_2}$; tension on the rear object $T=m_{2}a$.

Cart activity

Same distance from rest: $\frac{a_2}{a_1}=\frac{T_1^2}{T_2^2}$

First law

Net force $=0$ ⇔ acceleration $=0$ (rest or constant velocity).

How Forces Affect Motion: diagrams to practise

Practise each one on paper: draw it from the checklist, then tick off every label.

How the school exam asks How Forces Affect Motion

The question patterns to expect, and the method that works for each.

Tricks to remember How Forces Affect Motion

Short memory aids. Say each one aloud once, then use it on a question the same day.

• Lazy, Push, Pair

  First law: objects are lazy (inertia). Second law: push harder, go faster ($F=ma$). Third law: forces come in pairs.

  Use it when: Recalling the three laws in order.

• Same object cancels, different objects don't

  Balanced forces sit on one object; action and reaction sit on two.

  Use it when: Assertion-reason questions on why action-reaction forces do not cancel.

• Give it time

  Stretch the stopping time, shrink the force: hands back, airbags, mats, bubble wrap.

  Use it when: Safety and catching questions.

• 1 N is an apple

  A 100 g apple pushes on your palm with about 1 N.

  Use it when: Sense-checking answers.

• Glue them together

  For tied objects, add the masses and use only outside forces.

  Use it when: System problems.

How Forces Affect Motion: exam-level solved questions

Ordered from exam level to HOTS. Cover the solution, write your own, then compare step by step.

Case-study practice (Section E style)

Read the situation, then answer every part. In a school exam set on the board pattern this is a 4-mark question split into 1 + 1 + 2 marks.

Where the marks are

How a typical answer is split into step marks. Show every step: a right final answer alone rarely earns full marks.

Where students lose marks in How Forces Affect Motion

The slips examiners see most often, and what to write instead.

• ✗Mistake: Thinking constant velocity needs a net force

  Everyday experience: we must keep pushing to keep things moving.

  Wrong working

  A car moves at a steady 60 km h${}^{-1}$, so the engine force is greater than friction.

  Right working

  At constant velocity the net force is zero: the engine's forward force equals friction and air resistance.

  ✓Do this: Net force changes velocity; it is not needed to keep velocity.

  Usually costs: 1 to 2 marks.

• ✗Mistake: Saying action and reaction cancel

  They are equal and opposite, like balanced forces.

  Wrong working

  The horse pulls the cart and the cart pulls the horse equally, so nothing can move.

  Right working

  The two forces act on different objects. The cart moves because the horse's pull on it is greater than the friction on the cart.

  ✓Do this: Always name the object each force acts on.

  Usually costs: The reasoning mark.

• ✗Mistake: Using mass for weight or forgetting g

  Mass and weight are mixed up in daily speech.

  Wrong working

  A 30 kg barbell needs a 30 N force to hold.

  Right working

  $W=mg=30\times 9.8=294$ N.

  ✓Do this: Force in newtons; mass in kilograms; multiply by $g$ for weight.

  Usually costs: 1 mark.

• ✗Mistake: Using the applied force instead of the net force in $F=ma$

  Friction is forgotten.

  Wrong working

  Push 55 N on a 25 kg block with 50 N friction: $a=\frac{55}{25}=2.2$ m s${}^{-2}$.

  Right working

  Net force $=55-50=5$ N; $a=\frac{5}{25}=0.2$ m s${}^{-2}$.

  ✓Do this: Find the net force first.

  Usually costs: The whole numerical.

• ✗Mistake: Losing units and powers in conversions

  Grams and centimetres are left as they are.

  Wrong working

  Bullet of 50 g stops in 50 cm: $F=50\times a$ with $s=50$.

  Right working

  Use $m=0.05$ kg and $s=0.5$ m before substituting.

  ✓Do this: Convert to kg, m, s first.

  Usually costs: The answer mark, sometimes the method mark.

NCERT exercise guide: How Forces Affect Motion

What each exercise in the NCERT chapter tests, how to approach it, and a question of the same kind solved step by step. Questions here are written in our own words.

Practice questions on How Forces Affect Motion

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

1. Q1 · 1 mark · MCQExam level

   The SI unit of force is
   (a) kg m s⁻¹
   (b) kg m s⁻²
   (c) kg m² s⁻²
   (d) kg s⁻²

   Hint

   Mass × acceleration.

   Answer

   (b) kg m s⁻² (the newton)

2. Q2 · 1 mark · MCQExam level

   Passengers in a bus fall backwards when it starts suddenly. This is due to
   (a) friction
   (b) inertia of rest
   (c) third law
   (d) gravity

   Hint

   The body wants to stay where it was.

   Answer

   (b) inertia of rest

3. Q3 · 1 mark · Assertion-reasonExam level

   Assertion (A): A toy car of 100 g moving at a constant 0.5 m s⁻¹ has no net force on it.
   Reason (R): Net force is needed only to change velocity.
   (a) A and R are both true, and R explains A correctly.
   (b) A and R are both true, but R does not explain A.
   (c) A is true, R is false.
   (d) A is false, R is true.

   Hint

   First law.

   Answer

   (a)

4. Q4 · 2 marks · Very short answerExam level

   Find the weight of a 50 kg student and the force a floor exerts on her when she stands still. Name this force.

   Hint

   $W=mg$.

   Answer

   $W=50\times 9.8=490$ N downwards; the floor pushes up with 490 N, the normal force.

5. Q5 · 3 marks · Short answerHarder exam level

   A 40 kg crate on a floor with 60 N friction is pushed with 80 N from rest. Find its acceleration and the distance moved in 4 s.

   Hint

   Net force first.

   Answer

   Net force $=20$ N; $a=\frac{20}{40}=0.5$ m s⁻²; $s=\frac{1}{2}\times 0.5\times 16=4$ m.

6. Q6 · 2 marks · Very short answerHarder exam level

   A 30 kg boy and a 45 kg man sit on identical sledges on smooth ice, and each is pushed with a force of 90 N. Find the acceleration of each and the ratio of their accelerations.

   Hint

   $a=\frac{F}{m}$.

   Answer

   Boy: $a=\frac{90}{30}=3$ m s⁻²; man: $a=\frac{90}{45}=2$ m s⁻². Ratio $3:2$, the inverse of the mass ratio $30:45$.

7. Q7 · 3 marks · Short answerHarder exam level

   When a person steps from a small rowing boat onto a jetty, the boat drifts away from the jetty. Why does this happen, and why does a large ship not move noticeably when a person steps off it?

   Hint

   Third law, then $a=\frac{F}{m}$.

   Answer

   To step forward, the person pushes backwards on the boat; the boat pushes the person forwards with an equal force (third law). The backward push on the light boat gives it a noticeable acceleration away from the jetty. The same push on a ship of huge mass gives a tiny acceleration, which is not noticed.

8. Q8 · 2 marks · Very short answerHarder exam level

   Why does a fire fighter have to hold a hose pipe firmly when water gushes out at high speed?

   Hint

   Water pushed forward.

   Answer

   The pipe pushes water forward with a large force; by the third law, the water pushes the pipe backward with an equal force, which can throw the pipe back unless held firmly.

9. Q9 · 3 marks · Short answerHarder exam level

   Velocity-time graphs of four objects are: P, a horizontal line above the time axis; Q, a line along the time axis; R, a straight line rising; S, a straight line falling to zero. On which objects does a net force act, and in which direction?

   Hint

   Is the velocity changing?

   Answer

   P (constant velocity) and Q (at rest): no net force. R is speeding up, so a net force acts in the direction of motion; S is slowing down, so a net force acts opposite to its motion.

10. Q10 · 3 marks · Short answerHarder exam level

    Two boxes of 2 kg and 6 kg are tied with a string on a smooth floor. A 24 N force pulls the 2 kg box. Find the acceleration and the tension. What would the tension be if the force pulled the 6 kg box instead?

    Hint

    Tension pulls only the rear box.

    Answer

    $a=\frac{24}{8}=3$ m s⁻². Rear box 6 kg: $T=6\times 3=18$ N. If the 6 kg box is pulled, the rear box is 2 kg: $T=2\times 3=6$ N (same acceleration).

11. Q11 · 3 marks · Short answerHOTS / competency

    A child on roller skates squirts a powerful toy water gun forwards and rolls backwards a little. A fire engine shooting a far stronger jet of water does not roll back. Explain both using Newton's laws.

    Hint

    Reaction force, mass and other forces.

    Answer

    The gun pushes water forwards, so the water pushes the gun (and child) backwards with an equal force (third law). The child has small mass and the skates give little friction, so this force produces a noticeable backward acceleration (second law). The fire engine has a huge mass and its brakes and tyre friction supply a forward force that balances the reaction, so the net force on it is zero and it stays at rest.

12. Q12 · 3 marks · Short answerHOTS / competency

    In a world with no friction at all, describe two things that would become impossible and one that would become easier. Use Newton's laws.

    Hint

    Walking pushes the ground backwards.

    Answer

    Walking would be impossible: your foot would slip back because the ground could not push you forward (third law needs friction here). Stopping a moving vehicle with brakes would be impossible; it would keep moving (first law). Easier: once started, a sliding object would keep moving without any push, so no energy would be wasted overcoming friction.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1. 1.What is the SI unit of force and how is it written?Show answer

   The newton, written in lower case; symbol N.

2. 2.When are forces on an object balanced?Show answer

   When their net force is zero, so the motion does not change.

3. 3.In which direction does friction act?Show answer

   Opposite to the motion (or to the tendency to move) between the surfaces.

4. 4.State Newton's first law.Show answer

   An object stays at rest or moves with constant velocity unless a net force acts on it.

5. 5.What is inertia?Show answer

   The tendency of an object to resist a change in its state of rest or uniform motion; it increases with mass.

6. 6.Define one newton.Show answer

   The force that gives a 1 kg mass an acceleration of 1 m s⁻².

7. 7.What is momentum?Show answer

   Mass × velocity, in the direction of the velocity.

8. 8.Why does a fielder pull the hands back while catching?Show answer

   It increases the stopping time, reducing the deceleration and the force on the hands.

9. 9.Do action and reaction act on the same object?Show answer

   No; they act on two different objects.

10. 10.Write the acceleration of two tied objects pulled by force F on a smooth surface.Show answer

    $a=\frac{F}{m_1+m_2}$.

Quick revision checklist

The night before the exam: can you do each of these without looking?

• ☐Can you find the net force for forces in the same and opposite directions?
• ☐Can you explain why a pushed box stops when you let go?
• ☐Can you state all three laws exactly?
• ☐Can you give three everyday examples of inertia?
• ☐Can you define one newton and calculate weight?
• ☐Can you solve a problem that needs net force, then $a$, then distance?
• ☐Can you explain airbags and catching using the second law?
• ☐Can you identify the action-reaction pair in walking, rowing and rockets?
• ☐Can you calculate recoil accelerations?
• ☐Can you find the acceleration and tension for two tied boxes?

How Forces Affect Motion: frequently asked questions