MCAT high-yield physics equations

Define displacement in kinematics.

Displacement is the change in position of an object. It is a vector quantity, having both magnitude and direction.

What is the equation for gravitational force?

$\displaystyle F = \\frac{G m_1 m_2}{r^2}$, where $\displaystyle G$ is the gravitational constant, $\displaystyle m_1$ and $\displaystyle m_2$ are masses, $\displaystyle r$ is distance.

True or False: Velocity is the same as speed.

False. Velocity is speed with a direction; speed is scalar.

Identify the equation of motion with constant acceleration.

$\displaystyle d = v_i t + \\frac{1}{2} a t^2$, where $\displaystyle d$ is distance, $\displaystyle v_i$ is initial velocity, $\displaystyle a$ is acceleration, $\displaystyle t$ is time.

Fill in the blank: The unit of force is _____.

Newton (N) is the unit of force.

How does mass affect acceleration?

Mass and acceleration are inversely related via $\displaystyle F = ma$. More mass means less acceleration for the same force.

Calculate final velocity: $\displaystyle v_i = 10 \, \text{m/s}, \ a = 2 \, \text{m/s}^2, \ t = 3 \, \text{s}$.

$\displaystyle v_f = v_i + a t = 10 + (2)(3) = 16 \, \text{m/s}$.

What does Newton's second law state?

$\displaystyle F = ma$, meaning force equals mass times acceleration.

True or False: An object in motion stays in motion unless acted on by a force.

True. This is Newton's first law of motion.

What is the formula for uniform acceleration?

$\displaystyle v_f^2 = v_i^2 + 2ad$, where $\displaystyle d$ is displacement.

Cause → Effect: Increasing force while mass remains constant.

Effect: Acceleration increases according to $\displaystyle a = \\frac{F}{m}$.

Identify the relationship between distance, speed, and time.

$\displaystyle d = vt$, where $\displaystyle d$ is distance, $\displaystyle v$ is speed, $\displaystyle t$ is time.

What are the components of projectile motion?

Horizontal and vertical motions are independent. Horizontal motion is constant; vertical motion has constant acceleration due to gravity.

Define acceleration in kinematics.

Acceleration is the rate of change of velocity over time, represented as $\displaystyle a = \\frac{\Delta v}{t}$.

Compare average speed and instantaneous speed.

Average speed is total distance over total time. Instantaneous speed is speed at a specific moment.

What factors determine the net force on an object?

Net force is determined by all individual forces acting on the object, vectorially summed.

Work-energy principle

The work done on an object equals the change in its kinetic energy: $\displaystyle W = riangle KE = KE_{final} - KE_{initial}$.

Define work in physics.

Work is the product of force and displacement in the direction of the force: $\displaystyle W = F imes d imes ext{cos}( heta)$.

True or False: Work can be negative.

True. Work is negative when the force and displacement are in opposite directions.

Kinetic energy formula?

Kinetic energy ($\displaystyle KE$) is given by $\displaystyle KE = \frac{1}{2} mv^2$, where $\displaystyle m$ is mass and $\displaystyle v$ is velocity.

Fill in the blank: Potential energy depends on ______.

Position relative to a reference point, typically height above the ground for gravitational potential energy.

Conservation of energy principle?

Energy cannot be created or destroyed; it can only be transformed from one form to another.

Calculate work done: F = 10 N, d = 5 m.

Work $\displaystyle W = F imes d = 10 ext{ N} imes 5 ext{ m} = 50 ext{ J}$.

Power formula?

Power ($\displaystyle P$) is the rate of doing work: $\displaystyle P = \frac{W}{t}$, where $\displaystyle t$ is time.

Potential energy formula?

Gravitational potential energy ($\displaystyle PE$) is given by $\displaystyle PE = mgh$, where $\displaystyle m$ is mass, $\displaystyle g$ is acceleration due to gravity, $\displaystyle h$ is height.

Question: What is power in terms of energy?

Power can also be defined as the rate of energy transfer: $\displaystyle P = \frac{E}{t}$.

Difference between kinetic and potential energy?

Kinetic energy is energy of motion; potential energy is stored energy based on position.

True or False: Energy is always conserved in closed systems.

True. In isolated systems, total energy remains constant, though it may change forms.

When is work zero?

Work is zero when the force is perpendicular to the displacement or when there is no displacement.

Identify the unit of power.

The unit of power is the Watt (W), where $\displaystyle 1 ext{ W} = 1 ext{ J/s}$.

Example of energy transformation.

A falling object converts gravitational potential energy to kinetic energy as it descends.

Calculate potential energy: m = 5 kg, h = 10 m.

Potential energy $\displaystyle PE = mgh = 5 ext{ kg} imes 9.8 ext{ m/s}^2 imes 10 ext{ m} = 490 ext{ J}$.