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Physics with Calculus: Key Concepts and Formulas from Chapters 1, 3, 4 & 5

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Termini in questo insieme (25)

  • Definition of displacement

    Displacement is the vector quantity that represents the change in position of an object, defined as the final position minus the initial position.

  • Average velocity formula

    Average velocity is displacement divided by time interval, given by \(\vec{v}_{avg} = \frac{\Delta \vec{x}}{\Delta t}\).

  • Instantaneous velocity definition

    Instantaneous velocity is the velocity of an object at a specific instant, defined as the derivative of position with respect to time: \(\vec{v} = \frac{d\vec{x}}{dt}\).

  • Acceleration definition

    Acceleration is the rate of change of velocity with respect to time, expressed as \(\vec{a} = \frac{d\vec{v}}{dt}\).

  • Kinematic equation for velocity with constant acceleration

    The velocity at time t is \(v = v_0 + at\), where v_0 is initial velocity and a is constant acceleration.

  • Kinematic equation for displacement with constant acceleration

    Displacement is given by \(x = x_0 + v_0 t + \frac{1}{2} a t^2\), where x_0 is initial position.

  • Velocity squared formula under constant acceleration

    The relation between velocity and displacement is \(v^2 = v_0^2 + 2a(x - x_0)\).

  • Definition of projectile motion

    Projectile motion describes the motion of an object thrown or projected into the air, subject only to gravity and air resistance neglected.

  • Horizontal and vertical components of projectile velocity

    Horizontal velocity is constant: \(v_x = v_0 \cos \theta\). Vertical velocity changes: \(v_y = v_0 \sin \theta - g t\).

  • Range of a projectile formula

    The horizontal range is \(R = \frac{v_0^2 \sin 2\theta}{g}\), where v_0 is initial speed and \(\theta\) is launch angle.

  • Definition of Newton's First Law

    Newton's First Law states that an object at rest or in uniform motion remains so unless acted upon by a net external force.

  • Newton's Second Law formula

    Newton's Second Law relates force and acceleration: \(\vec{F} = m \vec{a}\), where m is mass.

  • Newton's Third Law statement

    Newton's Third Law states that for every action, there is an equal and opposite reaction.

  • Definition of friction force

    Friction is the force opposing relative motion between surfaces, proportional to the normal force: \(f = \mu N\).

  • Work done by a constant force

    Work is the product of force and displacement in the direction of the force: \(W = F d \cos \theta\).

  • Kinetic energy formula

    Kinetic energy is the energy of motion: \(K = \frac{1}{2} m v^2\).

  • Potential energy near Earth's surface

    Gravitational potential energy is \(U = m g h\), where h is height above reference point.

  • Work-Energy Theorem

    The Work-Energy Theorem states that net work done on an object equals its change in kinetic energy: \(W_{net} = \Delta K\).

  • Power definition and formula

    Power is the rate of doing work: \(P = \frac{W}{t}\).

  • Impulse and momentum relation

    Impulse equals change in momentum: \(\vec{J} = \Delta \vec{p} = \vec{F} \Delta t\).

  • Definition of momentum

    Momentum is the product of mass and velocity: \(\vec{p} = m \vec{v}\).

  • Conservation of momentum principle

    Momentum of a closed system remains constant if no external forces act on it.

  • Definition of uniform circular motion

    Uniform circular motion is motion in a circle at constant speed, with acceleration directed toward the center.

  • Centripetal acceleration formula

    Centripetal acceleration is \(a_c = \frac{v^2}{r}\), directed toward the center of the circle.

  • Centripetal force formula

    Centripetal force required for circular motion is \(F_c = m \frac{v^2}{r}\).