Motion and Force (RRB)

Motion is a change of position with time.

Scalar vs vector:

• Scalars have magnitude only: distance, speed, mass, time.
• Vectors have magnitude and direction: displacement, velocity, acceleration, force.

Speed = distance / time (scalar). Velocity = displacement / time (vector). On a straight road they have the same magnitude; on a circle, after one full lap, displacement = 0 → average velocity = 0 even though average speed > 0.

Acceleration = rate of change of velocity. Unit: m/s². Negative acceleration is retardation or deceleration.

Equations of uniformly accelerated motion (a = constant):

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

Here u = initial velocity, v = final, s = displacement, a = acceleration, t = time.

Newton's three laws of motion:

• First law (inertia): a body at rest stays at rest, and a body in uniform motion stays in motion, unless an external force acts. Mass is a measure of inertia.
• Second law: Force = mass × acceleration. F = ma. Unit: newton (N) = kg·m/s².
• Third law: For every action there is an equal and opposite reaction. The two forces act on different bodies.

Momentum (p) = mass × velocity. Unit: kg·m/s. F = dp/dt (force = rate of change of momentum). For constant mass, F = ma.

Conservation of momentum: in the absence of external forces, total momentum of an isolated system is constant. Foundation of rocket propulsion, recoil of guns, collisions.

Friction: opposes relative motion. Types: static (before motion), kinetic (during motion), rolling (smallest). Friction depends on normal force and surface roughness, not on area.

Free fall: in a gravitational field, all objects accelerate at g = 9.8 m/s² (downward), regardless of mass — if air resistance is negligible.

Example 1 — Free fall:
A stone is dropped from a 45 m tall building. Time to reach the ground? (g = 10 m/s²)
Method: s = ut + ½gt² → 45 = 0 + ½×10×t² → t² = 9 → t = 3 s.

Example 2 — Newton's second law:
A force of 20 N accelerates an object at 4 m/s². Find its mass.
Method: F = ma → m = 20/4 = 5 kg.

Example 3 — Momentum:
A 0.5 kg cricket ball moving at 30 m/s is caught and stopped in 0.05 s. Average force on the hands?
Method: Change in momentum = 0.5 × 30 = 15 kg·m/s. Force = Δp/Δt = 15/0.05 = 300 N.

Example 4 — Equation of motion:
A train accelerates from rest at 0.5 m/s² for 60 s. Velocity attained and distance covered?
Method: v = u + at = 0 + 0.5×60 = 30 m/s. s = ut + ½at² = 0 + ½×0.5×60² = 900 m.

Common RRB facts to recall:

• 1 N (newton) is the force needed to accelerate 1 kg at 1 m/s².
• 1 kgf (kilogram-force) = 9.8 N (weight of 1 kg on Earth's surface).
• The SI unit of pressure is the pascal (Pa) = 1 N/m².
• Centripetal force keeps an object in circular motion; magnitude = mv²/r, directed toward the centre.
• Centrifugal "force" is the apparent outward force felt in a rotating frame — not a real force.
• A satellite stays in orbit when gravity provides exactly the centripetal force it needs.

Newton's first law explains:

• Why you lurch forward when a bus brakes.
• Why a ball rolling on a smooth floor takes time to stop (friction stops it).
• Why a coin on a card on a glass falls into the glass when the card is flicked away (inertia).