Mechanics and Motion Questions for NDA

Basic Kinematics: Equations of Motion

Kinematics deals with describing motion without worrying about its cause. For uniformly accelerated motion in a straight line, three equations connect initial velocity, final velocity, acceleration, time, and displacement. These are your most-used tools in NDA Physics. Remember: these equations apply only when acceleration is constant.

• v = u + at (velocity-time relation)
• s = ut + half at squared (displacement-time relation)
• v squared = u squared + 2as (velocity-displacement relation)
• nth second formula: s_n = u + a(2n-1)/2 gives displacement in the nth second
• Acceleration due to gravity g = 9.8 m/s squared, often rounded to 10 in NDA for quick calculation
• For free fall: u = 0, a = g downward; for upward throw: a = -g

Projectile Motion

A projectile is any object thrown at an angle under gravity alone. The key insight is: horizontal and vertical motions are independent. Horizontal: constant velocity (no acceleration). Vertical: uniform acceleration g downward. NDA frequently asks for range, maximum height, and time of flight. Angle of 45 degrees always gives maximum range.

• Horizontal velocity component: u cos(theta), stays constant throughout flight
• Vertical velocity component: u sin(theta), decreases going up, increases coming down
• Time of flight: T = 2u sin(theta) / g
• Maximum height: H = u squared sin squared(theta) / 2g
• Horizontal range: R = u squared sin(2 theta) / g
• Maximum range at theta = 45 degrees: R_max = u squared / g

Newton's Laws of Motion

Newton's three laws form the foundation of all mechanics. NDA tests them both as concepts and calculations. First law defines inertia. Second law connects force, mass, and acceleration. Third law is about action-reaction pairs. The most common NDA application is free body diagrams for connected bodies, pulleys, and inclined planes.

• First law (Inertia): A body continues in its state unless external net force acts
• Second law: F = ma. Net force equals mass times acceleration
• Third law: Every action has an equal and opposite reaction. Forces act on different bodies
• For connected bodies on a table with a hanging mass: a = Mg / (M + m), T = Mm g / (M + m)
• On inclined plane: component of gravity along plane = mg sin(theta), normal force = mg cos(theta)
• Impulse = Force x time = change in momentum (F x t = mv - mu)

Work, Energy, and Power

Work is done only when force causes displacement in its own direction. Energy comes in kinetic and potential forms, and the work-energy theorem connects them directly. NDA often asks about conservation of energy and power calculations. Remember: work can be zero even if force is applied (perpendicular force does no work).

• Work W = Fs cos(theta), where theta is angle between force and displacement
• Kinetic energy KE = half mv squared
• Potential energy PE = mgh (gravitational)
• Work-energy theorem: Net work done = change in KE
• Power P = Work / time = Fv (force times velocity)
• In elastic collision: both KE and momentum conserved. In perfectly inelastic: only momentum conserved

Circular Motion and Centripetal Force

Circular motion involves a constantly changing direction of velocity. The acceleration always points toward the center (centripetal). NDA asks about banking of roads, minimum speed at top of loops, and the difference between centripetal and centrifugal force. Centrifugal force is a pseudo force felt only in rotating frames.

• Centripetal acceleration: a = v squared / r = omega squared r
• Centripetal force: F = mv squared / r, always directed toward center
• For a car on a curved road: friction provides centripetal force, max speed = sqrt(mu r g)
• For a banked road: tan(theta) = v squared / rg
• At top of vertical loop, minimum speed: v = sqrt(rg) so that mg provides centripetal force
• Angular velocity omega = 2 pi / T = 2 pi f

• Using g = 9.8 when the problem implies 10, or mixing both in one solution. In NDA, unless stated otherwise, use g = 10 m/s squared for speed.
• In projectile motion, forgetting that range formula uses sin(2 theta), not sin(theta). Writing sin(theta) instead of sin(2 theta) is a very common error.
• Confusing complementary angles: 30 and 60 degrees give the same range but different heights and flight times. Questions often test this distinction.
• Treating centrifugal force as a real force in an inertial frame. It is a pseudo force valid only in rotating frames of reference.
• In work formula W = Fs cos(theta), taking theta as the angle of incline instead of the angle between force and displacement direction.

• SUVAT mnemonic for kinematics variables: S = displacement, U = initial velocity, V = final velocity, A = acceleration, T = time. Pick the equation that has your 4 known variables.
• For projectile: THRT = Time uses sin, Height uses sin squared, Range uses sin 2theta. Remember THR order.
• Newton laws: 1 = Lazy body stays put (inertia), 2 = Force wakes it up (F=ma), 3 = Every push gets a push back (action-reaction).
• Work is ZERO when force is perpendicular to motion (like normal force on a flat surface, or moon orbiting Earth). Visualize pushing a wall: effort yes, work no.

• NDA typically has 2-3 direct formula questions from kinematics and 1-2 from projectile motion every paper. These are the easiest marks in Physics if formulas are memorized cold.
• Conceptual questions on Newton's third law and inertia appear frequently in GAT as one-liners. Read all options carefully as they often differ by just one word like 'same body' vs 'different bodies'.
• Circular motion and banking questions are medium difficulty and often involve a two-step calculation. Do not rush: find centripetal force first, then equate to friction or normal component.
• Energy conservation questions on inclined planes and loops are high-value. They avoid complex algebra if you use energy methods instead of kinematics equations.
• Timing tip: A standard mechanics numerical should take 60-90 seconds. If it goes beyond 2 minutes, mark it and move on. Most of these have answer choices that let you eliminate with rough estimates.