NCERT Science: Motion, Force and Gravitation

The one-line takeaway

Motion is the change of position with time, described by distance, displacement, speed, velocity and acceleration. Force is what changes a body's state of motion, governed by Newton's three laws, and momentum (mass times velocity) is conserved when no external force acts. Gravitation is the universal attraction between masses, which gives weight and holds the solar system together.

Describing motion

• Distance is the total path length (a scalar, magnitude only). Displacement is the shortest straight-line distance from start to finish with direction (a vector). Displacement can be zero even when distance is not, as in a round trip.
• Speed is distance per unit time (a scalar); velocity is displacement per unit time (a vector). The SI unit of both is the metre per second.
• Acceleration is the rate of change of velocity; SI unit metre per second squared. It is positive when speeding up and negative (retardation) when slowing down.
• Uniform motion covers equal distances in equal times; non-uniform motion does not. On a distance-time graph, the slope gives speed; on a velocity-time graph, the slope gives acceleration and the area under the line gives distance.

The equations of motion (for uniform acceleration)

For a body with initial velocity u, final velocity v, acceleration a, time t and distance s:

• v = u + at
• s = ut + half a t squared
• v squared = u squared + 2as

These are recognition-level facts for CAPF, not derivations.

Newton's laws of motion

• First law (law of inertia): a body continues at rest or in uniform motion in a straight line unless acted upon by an external unbalanced force. Inertia is the tendency to resist change in the state of motion, and it increases with mass. This explains why passengers lurch forward when a bus brakes.
• Second law: the rate of change of momentum is proportional to the applied force and in its direction. For constant mass this gives force equals mass times acceleration (F = ma). The SI unit of force is the newton (the force that gives a one-kilogram mass an acceleration of one metre per second squared).
• Third law: to every action there is an equal and opposite reaction; the two act on different bodies. This explains recoil of a gun, the walking push against the ground, and rocket and jet propulsion.

Momentum

• Momentum is the product of mass and velocity (a vector); SI unit kilogram metre per second.
• Conservation of momentum: in the absence of an external force, the total momentum of a system stays constant. This is why a fired gun recoils, why a rocket moves forward as gas is expelled backward, and why two colliding bodies share momentum.

Gravitation

• Newton's universal law of gravitation: every body attracts every other body with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them.
• Acceleration due to gravity (g) on Earth is about 9.8 metre per second squared. It is slightly greater at the poles than at the equator, and it decreases with altitude and depth. On the Moon, g is about one-sixth of Earth's.
• Mass is the amount of matter in a body and is constant everywhere; weight is the force of gravity on it (mass times g) and changes with location. A body weighs less on the Moon.
• Free fall: a body falling under gravity alone. In a vacuum, all bodies fall at the same rate regardless of mass (the feather-and-coin demonstration), because g is the same for all.
• Gravitation explains tides (the Moon's and Sun's pull on the oceans), the orbits of planets and satellites, and why objects have weight.

Key terms to fix

• Distance versus displacement: total path (scalar) versus shortest straight line with direction (vector).
• Newton's three laws: inertia; F = ma; action-reaction.
• Newton (N): the SI unit of force.
• Momentum and its conservation: mass times velocity, conserved without external force.
• g approximately 9.8 metre per second squared; mass is constant, weight varies.

CAPF angle

Newton's third law is the principle behind firearm recoil, rocket and missile propulsion, and jet engines, all central to defence technology. Momentum and ballistics underlie marksmanship and projectile behaviour. Gravitation governs satellite orbits, the basis of reconnaissance, navigation (the Indian regional navigation system NavIC) and communications that the forces depend on. The physics of free fall is relevant to parachuting and airborne operations.

Authored practice