ECAT flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Newton's Second Law

The net force acting on an object equals the product of its mass and acceleration, written as F = ma; force and acceleration point in the same direction.

Projectile Motion

Two-dimensional motion under gravity alone, where horizontal velocity remains constant and vertical motion accelerates at g downward, producing a parabolic path.

Ohm's Law

The current through a conductor is directly proportional to the potential difference across it and inversely proportional to its resistance, V = IR.

Work-Energy Theorem

The net work done on an object equals the change in its kinetic energy, so W = ½mv² − ½mu² for a mass changing speed from u to v.

Total Internal Reflection

Light traveling from a denser to a rarer medium beyond the critical angle is entirely reflected back inside the denser medium instead of refracting out.

Conservation of Momentum

In an isolated system with no external net force, the total momentum before a collision equals the total momentum after it, regardless of whether the collision is elastic.

Pendulum Period

For small swings, a simple pendulum's period is T = 2π√(L/g), depending on length and gravity but not on the bob's mass or amplitude.

Resistors in Parallel

For resistors connected side by side, the reciprocal of total resistance equals the sum of reciprocals: 1/R = 1/R₁ + 1/R₂ + ...

Mole Concept

One mole of any substance contains 6.022 × 10²³ representative particles, and its mass in grams equals its molar mass.

Molar Volume at STP

At standard temperature and pressure, one mole of any ideal gas occupies approximately 22.4 liters, regardless of the gas's identity.

pH Scale

pH equals the negative logarithm of hydrogen ion concentration; values below 7 are acidic, above 7 basic, and pH plus pOH equals 14 at 25 °C.

Le Chatelier's Principle

When a system at equilibrium is disturbed by a change in concentration, pressure, or temperature, it shifts in the direction that partially counteracts the disturbance.

Oxidation and Reduction

Oxidation is loss of electrons and an increase in oxidation number; reduction is gain of electrons and a decrease in oxidation number; both occur together in redox reactions.

Ideal Gas Law

The pressure and volume of a gas are related by PV = nRT, where n is moles, R is the gas constant, and T must be expressed in kelvin.

Periodic Atomic Radius Trend

Atomic radius generally decreases from left to right across a period as nuclear charge grows, and increases down a group as extra electron shells are added.

Balancing Redox in Acid

Balance atoms other than O and H first, then oxygen with water molecules, hydrogen with H⁺ ions, and finally charge by adding electrons.

Quadratic Formula

For ax² + bx + c = 0 with a ≠ 0, the solutions are x = [−b ± √(b² − 4ac)] / (2a), where the discriminant b² − 4ac sets the root type.

Sum and Product of Roots

For a quadratic ax² + bx + c = 0, the two roots add to −b/a and multiply to c/a, allowing roots to be found from coefficients.

Pythagorean Trigonometric Identity

For any angle θ, sin²θ + cos²θ = 1; dividing by cos²θ or sin²θ yields the related identities involving tan, sec, and csc.

Power Rule for Derivatives

The derivative of x raised to a constant power n is n times x raised to the power n − 1, valid for all real n.

Product Rule

The derivative of a product uv equals u′v plus uv′, where u′ and v′ are the derivatives of the two factors.

Arithmetic Series Sum

The sum of the first n terms of an arithmetic sequence is Sₙ = (n/2)[2a + (n−1)d], where a is the first term and d the common difference.

Logarithm Product Rule

The logarithm of a product equals the sum of the logarithms of the factors, and the log of a power equals the exponent times the log of the base.

Distance Formula

The straight-line distance between two points (x₁,y₁) and (x₂,y₂) is the square root of (x₂−x₁)² plus (y₂−y₁)².

Subject-Verb Agreement

A verb must match its subject in number; phrases between the subject and verb do not change whether the subject is singular or plural.

Active Versus Passive Voice

In active voice the subject performs the action; in passive voice the object becomes the subject and the verb uses a form of 'be' plus a past participle.

Comma Splice

A comma splice incorrectly joins two independent clauses with only a comma; it is fixed with a period, a semicolon, or a coordinating conjunction.

Restrictive Clause

A clause giving essential information that identifies the noun is not set off by commas; a non-restrictive clause adds extra information and is comma-separated.

Affect Versus Effect

'Affect' is usually a verb meaning to influence, while 'effect' is usually a noun meaning a result or outcome.

Parallel Structure

Items joined in a list or comparison should share the same grammatical form, such as all gerunds or all infinitives, for clarity and correctness.

Indirect Speech Tense Shift

When converting direct to indirect speech, the reported verb typically shifts one tense back, and pronouns and time words adjust to the new context.

Its Versus It's

'Its' is the possessive form showing ownership, while 'it's' is a contraction of 'it is' or 'it has' and never shows possession.