IMU CET key terms

A quantity that has both magnitude and direction, such as displacement, velocity, or force. It is often represented by an arrow whose length shows magnitude and whose direction shows the direction of the quantity.

A physical quantity described by magnitude alone, without direction. Examples include mass, time, speed, and temperature. Scalars add by ordinary arithmetic, unlike vectors.

The single vector that produces the same effect as two or more vectors acting together. It is found by vector addition, for example using the parallelogram law or resolving into components.

The part of a vector along a chosen axis. A vector can be resolved into perpendicular components, usually horizontal and vertical, whose combined effect equals the original vector.

The rate at which a function changes with respect to its variable. Geometrically it is the slope of the tangent to the curve; in physics, velocity is the derivative of displacement with respect to time.

The continuous sum of a quantity over an interval, interpreted as the area under a curve. In physics, the integral of velocity over time gives displacement.

The value that a function approaches as its input approaches a particular point. Limits are the foundation of derivatives and integrals in calculus.

A single number computed from a square matrix that indicates whether the matrix is invertible. A zero determinant means the matrix has no inverse; determinants also appear in solving linear equations.

A rectangular array of numbers arranged in rows and columns. Matrices are used to represent systems of linear equations, transformations, and many engineering calculations.

A number between 0 and 1 expressing how likely an event is. For equally likely outcomes, it equals the number of favourable outcomes divided by the total number of outcomes.

An arrangement of items in which order matters. The number of permutations of n distinct items taken r at a time is n! divided by (n − r)!.

A selection of items in which order does not matter. The number of combinations of n items taken r at a time is n! divided by r!(n − r)!.

The net force on a body equals its mass times its acceleration (F = ma). It relates force, mass, and acceleration and is the basis for solving most dynamics problems.

The tendency of an object to resist changes in its state of motion. Mass is a measure of inertia; a larger mass requires a larger force to produce the same acceleration.

The product of an object's mass and its velocity (p = mv). It is a vector quantity; in an isolated system, total momentum is conserved in collisions.

The product of a force and the time interval over which it acts. Impulse equals the change in momentum of the body on which the force acts.

The turning effect of a force about a point, equal to force multiplied by the perpendicular distance from the point to the line of action of the force. It is measured in newton metres.

The turning effect of a force about a pivot, calculated as force times perpendicular distance. In equilibrium problems, the sum of clockwise moments equals the sum of anticlockwise moments.

The state of a body when the net force and net moment acting on it are both zero. The body then remains at rest or moves with constant velocity.

The upward force exerted by a fluid on an object immersed in it, equal to the weight of the fluid displaced. It explains why ships float and how submerged objects behave.

The law stating that the buoyant force on a body immersed in a fluid equals the weight of the fluid it displaces. It is fundamental to ship stability and flotation calculations.

The mass of a substance per unit volume, usually expressed in kilograms per cubic metre. An object floats in a fluid if its average density is less than that of the fluid.

The bending of light as it passes from one medium to another because its speed changes. It is described by Snell's law and explains effects such as a stick appearing bent in water.

The ratio of the speed of light in a vacuum to its speed in a medium. It determines how much light bends when entering or leaving the medium.

The amount of a substance containing Avogadro's number (about 6.022 × 10²³) of particles. It links the mass of a substance to the number of atoms or molecules present.

The mass of one mole of a substance, expressed in grams per mole. It is numerically equal to the relative atomic or molecular mass and is used to convert between mass and moles.

The number of particles in one mole of a substance, approximately 6.022 × 10²³ per mole. It connects microscopic particle counts with measurable macroscopic amounts.

The concentration of a solution expressed as moles of solute per litre of solution. It is widely used in titration and solution calculations.

A procedure for finding the concentration of a solution by adding a standard solution of known concentration until the reaction reaches its end point, often shown by an indicator colour change.

A scale from 0 to 14 measuring the acidity or alkalinity of a solution. Values below 7 are acidic, 7 is neutral, and above 7 are alkaline.

A substance that donates hydrogen ions (protons) in solution, or accepts an electron pair. Acids turn blue litmus red and react with bases to form salts and water.

A substance that accepts hydrogen ions (protons) or donates an electron pair. Bases turn red litmus blue and neutralise acids to form salts and water.

The grammatical rule that a verb must match its subject in number and person. A singular subject takes a singular verb; a plural subject takes a plural verb.

The form of a verb that shows the time of an action or state, such as past, present, or future. Correct tense use is essential for clear and accurate writing.

A sentence construction in which the subject performs the action of the verb, as in 'The crew secured the hatch.' It is usually clearer and more direct than the passive voice.

A sentence construction in which the subject receives the action of the verb, as in 'The hatch was secured by the crew.' It is formed with a form of 'be' plus the past participle.

A word that has the same or nearly the same meaning as another word in the same language, such as 'begin' and 'start'. Recognising synonyms is a common vocabulary test skill.

A word that has the opposite meaning to another word, such as 'hot' and 'cold'. Antonym questions test vocabulary range and precision.

A fixed expression whose meaning cannot be worked out from the individual words, such as 'to weather the storm'. Idioms are tested in English usage sections.

The angular distance of a point north or south of the equator, measured in degrees from 0° at the equator to 90° at the poles. It is used with longitude to fix a position on Earth.

The angular distance of a point east or west of the prime meridian, measured in degrees from 0° to 180°. It is used with latitude to specify a position on Earth.

The reference line of longitude passing through Greenwich, defined as 0° longitude. Longitudes are measured east or west from it up to 180°.

A circle on the surface of a sphere whose plane passes through the sphere's centre, dividing it into two equal halves. The shortest route between two points on Earth follows a great circle.

A line on the Earth's surface that crosses every meridian at the same angle, appearing as a straight line on a Mercator chart. It is not the shortest route but is easy to steer.

The direction of one point from another, usually measured clockwise from north in degrees from 000° to 360°. Bearings are used in navigation and position fixing.

The direction in which a vessel's bow is pointing at any moment, expressed as a compass bearing. It may differ from the course made good because of wind and current.

The intended direction of travel of a vessel from one position to another, expressed in degrees. It is planned on a chart and may need correction for leeway and current.

A unit of speed equal to one nautical mile per hour, approximately 1.852 kilometres per hour. It is the standard unit for expressing a vessel's speed.

A unit of distance used at sea, equal to 1,852 metres. It corresponds approximately to one minute of latitude and is used with the knot for speed calculations.

The left-hand side of a vessel when facing forward. The term is fixed regardless of the direction the vessel is facing and is marked by a red navigation light at night.

The right-hand side of a vessel when facing forward. It is marked by a green navigation light at night and takes priority in many collision-avoidance situations.

The vertical distance from the waterline to the lowest point of a vessel's keel. It determines the minimum depth of water in which the vessel can safely navigate.

The vertical distance from the waterline to the main deck at the side of a vessel. It indicates how much hull remains above water and affects reserve buoyancy.

The weight of water displaced by a floating vessel, equal to the weight of the vessel and everything on board. It is usually expressed in tonnes.

The total weight a vessel can carry, including cargo, fuel, fresh water, ballast, stores, and crew, when loaded to its maximum permitted draught. It is expressed in tonnes.