Motion and Force (RRB)

Why does a passenger lurch forward when a bus brakes hard? Why does a rocket rise by throwing gas downward? Why do all objects fall at the same rate in a vacuum, whatever their weight? Every one of these everyday puzzles is answered by motion and Newton's three laws — the foundation of all mechanics. This lesson builds the concepts and equations you need for Class 9–10 physics and railway/SSC General Science, with the intuition behind each rule, not just the formula.

Definition: Motion is a change in an object's position with time. To describe it we use two kinds of quantity: a scalar has magnitude only (distance, speed, mass, time), while a vector has magnitude and direction (displacement, velocity, acceleration, force).

The scalar/vector distinction is not a technicality — it is the source of some of the trickiest exam questions, because the direction information in a vector can make its average value zero even when the corresponding scalar is large.

Speed, velocity and acceleration

Speed = distance ÷ time, and it is a scalar — it tells you how fast, not which way. Velocity = displacement ÷ time, and it is a vector — it tells you how fast and in what direction. On a straight road the two have the same magnitude. But on a circular track, after one complete lap the object returns to its start, so its displacement is zero — which means its average velocity is zero even though its average speed is clearly not. This single idea is a perennial exam favourite.

Acceleration is the rate of change of velocity, measured in m/s². A positive acceleration speeds an object up; a negative acceleration (called retardation or deceleration) slows it down. Crucially, because velocity is a vector, an object moving at constant speed around a circle is still accelerating — its direction is changing.

For motion with constant acceleration, three equations govern everything you will be asked:

1. v = u + at
2. s = ut + ½at²
3. v² = u² + 2as

Here u = initial velocity, v = final velocity, s = displacement, a = acceleration, t = time. Choose the equation that contains the three quantities you know plus the one you want — that is the whole technique.

Newton's three laws of motion

• First law (the law of inertia): A body at rest stays at rest, and a body in uniform motion continues in a straight line at constant speed, unless an external unbalanced force acts on it. Mass is the measure of inertia — the more mass, the harder it is to start, stop or turn an object.
• Second law: The net force on a body equals its mass times its acceleration: F = ma. The SI unit of force is the newton (N), where 1 N = 1 kg·m/s². This law quantifies the first: it tells you how much acceleration a given force produces.
• Third law: For every action there is an equal and opposite reaction. The most important and most misunderstood part is the small print: the two forces act on different bodies.

Momentum, friction and free fall

Momentum (p) = mass × velocity, with unit kg·m/s, and it captures the "quantity of motion" a body carries. Newton's second law is, in its most general form, F = dp/dt — force is the rate of change of momentum — which reduces to F = ma when the mass is constant.

The conservation of momentum states that, in the absence of any external force, the total momentum of an isolated system stays constant. This single principle explains rocket propulsion (the rocket gains forward momentum equal and opposite to the momentum of the gas it expels), the recoil of a fired gun, and the outcome of collisions.

Friction is the force that opposes relative motion between surfaces in contact. It comes in three grades: static friction (before sliding begins) is the strongest, kinetic (sliding) friction is smaller, and rolling friction is the smallest of all — which is exactly why wheels were such a revolution. A key, counter-intuitive fact: friction depends on the normal force and the roughness of the surfaces, not on the contact area.

In free fall, with air resistance negligible, every object accelerates downward at g = 9.8 m/s² regardless of its mass. A feather and a coin dropped in a vacuum hit the ground together — the famous result confirmed on the Moon by Apollo astronauts.

Worked examples

Question: A car increases its velocity from 10 m/s to 30 m/s in 5 s. Find its acceleration.
Solution:
Step 1: Use v = u + at with u = 10, v = 30, t = 5.
Step 2: 30 = 10 + a×5 → 20 = 5a → a = 4.
Conclusion: The acceleration is 4 m/s².

Question: A 1000 kg car is pushed by a net force of 2000 N. How fast is it going after 6 s from rest?
Solution:
Step 1: Find acceleration from F = ma → a = F/m = 2000/1000 = 2 m/s².
Step 2: Use v = u + at = 0 + 2×6.
Conclusion: The car's speed is 12 m/s.

Why it matters: These principles underlie vehicle braking distances, seat-belt and airbag design, spaceflight and every machine that moves. F = ma alone lets engineers predict how hard a locomotive must push to reach a target speed in a given time — the kind of calculation behind real railway operation, and a recurring General Science topic.

Real-world example: When a moving bus brakes suddenly, your body keeps moving forward because of inertia (Newton's first law). Your feet stop with the bus, but your upper body — with no force acting to stop it — continues forward until a seat or handrail finally supplies that force. That same inertia is precisely why seat belts exist: the belt is the external force that decelerates you safely instead of the windscreen doing it abruptly.

Common misconception 1: That Newton's third-law action and reaction "cancel out", so nothing should ever move. They do not cancel, because the two equal-and-opposite forces act on different bodies. A rocket pushes gas down; the gas pushes the rocket up. Since each force acts on a separate object, the rocket genuinely accelerates. Forces only cancel when they act on the same body.

Common misconception 2: That heavier objects fall faster. In the absence of air resistance, all objects fall at the same g = 9.8 m/s². Heavier objects seem to fall faster on Earth only because air resistance affects light, spread-out objects (like a feather) more than dense ones.

:::compare Scalar vs vector

:::keypoints Key points

• Scalars have magnitude only; vectors have magnitude and direction.
• After a closed loop, displacement and average velocity are zero though speed is not.
• The three equations of motion apply only when acceleration is constant.
• F = ma; the newton equals kg·m/s²; mass measures inertia.
• Action–reaction forces are equal, opposite, and act on different bodies, so they don't cancel.
• Momentum = mv is conserved when no external force acts — the basis of rockets, recoil and collisions.
• Friction depends on normal force and roughness, not on contact area; rolling friction is smallest.
• In free fall (no air resistance) all objects accelerate at g = 9.8 m/s² regardless of mass.
  :::
  :::memory
• "Force on different bodies never cancels" — the rocket flies because action and reaction push two different things.
  :::
  :::recap
• Motion is described by speed/velocity/acceleration; only velocity is a vector.
• Newton's three laws explain inertia, force (F = ma), and action–reaction.
• Momentum is conserved when no external force acts on a system.
• Friction depends on roughness and normal force, not contact area.
• All objects free-fall at the same rate when air resistance is ignored.
  :::

Why do you lurch forward when a bus brakes, and why does a cricketer pull his hands back while catching a fast ball? Newton's three laws answer both, and the kinematic equations let you put precise numbers on the motion. This lesson works through force-and-motion problems exactly the way RRB and SSC exams frame them — fixed methods, only the numbers changing — so you can score these items almost automatically.

Definition: Force is a push or pull that can change an object's state of motion (its speed, direction, or both). Its SI unit is the newton (N) — the force that gives a 1 kg mass an acceleration of 1 m/s².
Definition: Momentum (p = mv) is the "quantity of motion" of a body. The net force on it equals the rate of change of its momentum: F = Δp/Δt. When mass is constant, this reduces to the familiar F = ma.

The three workhorse equations for constant acceleration appear in almost every numerical: v = u + at, s = ut + ½at², and v² = u² + 2as (u = initial velocity, v = final, s = displacement, a = acceleration, t = time). The entire skill is choosing the equation that contains your three knowns plus the one unknown.

Free fall — choosing the right kinematic equation

Question: A stone is dropped from a 45 m building. Find the time to reach the ground (g = 10 m/s²).
Solution:
Step 1: "Dropped" means the initial velocity u = 0. We know s = 45, a = g = 10, and want t, so use s = ut + ½gt².
Step 2: 45 = 0 + ½ × 10 × t² → 45 = 5t² → t² = 9.
Conclusion: t = 3 s.

The lesson of this example: the word "dropped" or "released" is a signal that u = 0, which simplifies the second equation dramatically.

Newton's second law

Question: A 20 N force accelerates an object at 4 m/s². Find its mass.
Solution:
Step 1: Newton's second law gives F = ma, so m = F/a.
Step 2: m = 20 / 4.
Conclusion: 5 kg.

F = ma is the most direct of all the relations — given any two of force, mass and acceleration, the third follows in one step.

Momentum and impulse

Question: A 0.5 kg cricket ball moving at 30 m/s is caught and stopped in 0.05 s. Find the average force on the hands.
Solution:
Step 1: The change in momentum Δp = m × Δv = 0.5 × 30 = 15 kg·m/s (the ball goes from 30 m/s to rest).
Step 2: Average force = Δp / Δt = 15 / 0.05.
Conclusion: 300 N.

This is impulse in action: impulse = force × time = change in momentum. The same momentum change spread over a longer time needs a smaller force — the key safety idea below.

A train accelerating from rest

A train accelerates from rest (u = 0) at 0.5 m/s² for 60 s.
Final velocity: v = u + at = 0 + 0.5 × 60 = 30 m/s.
Distance covered: s = ut + ½at² = 0 + ½ × 0.5 × 60² = ½ × 0.5 × 3600 = 900 m.
Two equations, one scenario — exactly the multi-part style RRB favours.

Key facts and circular motion

• 1 N accelerates 1 kg at 1 m/s²; 1 kgf (kilogram-force) = 9.8 N, the weight of 1 kg at Earth's surface.
• SI unit of pressure: the pascal (Pa) = 1 N/m².
• Centripetal force = mv²/r, directed toward the centre, is what keeps a body moving in a circle. Gravity (for a satellite), tension (for a whirled stone) or friction (for a turning car) can each supply it.
• The "centrifugal force" is only an apparent outward force felt in a rotating frame — it is not a real force.
• A satellite stays in orbit when gravity provides exactly the centripetal force the orbit requires — too little and it falls in, too much and it flies out.

Why it matters: Newton's laws govern everything that moves — vehicles, sports, machinery, rockets and satellites. The kinematic equations and F = ma are among the most reliable scoring topics in any physics section precisely because the method is fixed; once you recognise which equation fits the given data, only the arithmetic remains.

Real-world example: A cricketer "gives" with the ball while catching — pulling the hands back to lengthen the stopping time Δt. Because force = Δp/Δt, a longer time means a smaller force on the hands, preventing injury. The identical principle is why cars have crumple zones and airbags (both extend the collision time to cut the force on passengers) and why you bend your knees when you land from a jump.

Common misconception 1: That a real outward "centrifugal force" flings objects out during circular motion. In an inertial (non-rotating) frame there is no such force. What actually keeps an object on its circular path is the inward centripetal force (gravity, tension or friction). The outward feeling is simply inertia — the body's natural tendency to keep moving in a straight line (Newton's first law) — not a real outward pull.

Common misconception 2: That "deceleration" needs a different equation. It does not — deceleration is just negative acceleration. Use the same three equations with a as a negative number, and the maths handles the slowing automatically.

:::compare Centripetal vs centrifugal force

:::keypoints Key points

• F = ma; 1 newton accelerates 1 kg at 1 m/s²; 1 kgf = 9.8 N.
• Kinematics for constant acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
• "Dropped" or "from rest" means u = 0 — use it to simplify.
• Force = rate of change of momentum (F = Δp/Δt) — the basis of impulse.
• Spreading a momentum change over more time reduces the force (catching, crumple zones, airbags).
• Centripetal force = mv²/r points inward; centrifugal force is only apparent.
• A satellite stays in orbit when gravity equals the required centripetal force.
• Deceleration is just negative acceleration — same equations apply.
  :::

:::memory

• "Longer time, smaller force" — give with the ball, and Δp/Δt protects your hands.
  :::

:::recap

• Pick the kinematic equation that matches your knowns and the unknown asked.
• F = ma links force, mass and acceleration in a single step.
• Spreading a momentum change over more time lowers the force.
• Circular motion needs an inward (centripetal) force; "centrifugal" is apparent.
• "From rest" sets u = 0 and simplifies the working.
  :::