Kinematics, Work, and Energy

MCAT Prep: Physics and Math Part 1

Vectors

physical quantities with both magnitude and direction. Ex. force, velocity

Scalars

physical quantities that have magnitude, but no direction. Ex. mass, speed

Displacement

(Δx) the change in position that goes in a straight-line path from the initial position to the final position; independent of the path taken (SI unit: m)

Average velocity

Δx/Δt (SI units: m/s)

Acceleration

the rate of change of an object’s velocity; it is a vector quantity: Δv/Δt (SI units: m/s²)

Linear motion

v = v₀ + at

x = v₀t + (1/2)at²

v² = v₀² + 2ax

v̅ = (v₀ + v)/2

x = v̅t = [(v₀ + v)/2]t

time

When solving for _______, there will be two values: when the projectile is initially launched and when it impacts the ground

0

To find max height, remember that the vertical velocity of the projectile is ____ at the highest point of the path

Projectile motion

• vertical component of velocity = v sin θ

• horizontal component of velocity = v cos θ

sin

vertical component of velocity = v ___ θ

cos

horizontal component of velocity = v ___ θ

Static friction

is the force that must be overcome to set an object in motion. It has the formula: 0 ≤ f_s ≤ μ_sN

Kinetic friction

opposes the motion of objects moving relative to each other. It has the formula: f_k = μ_kN

constant

for a _______ force F acting on an object that moves a displacement of d, the work is W = Fd cos θ

perpendicular

for a force ________ to the displacement, W = 0

Work

SI unit: joule = N x m

by

When the piston expands, work is done ___ the system (W > 0)

one

When the piston compresses the gas, work is done ____ the system (W < 0)

P vs. V

The area under a ________ curve is the amount of work done in a system

Power

the rate at which work is performed; it is given by: W/Δt (SI unit: watt = J/S)

Energy

is a scalar quantity (SI unit: joule)

Kinetic energy

the energy associated with moving objects. It is given by: (1/2)mv²

Potential energy

the energy associated with a body’s position. Gravitational potential energy of an object is due to the force of gravity acting on it and is expressed as: U = mgh

Total mechanical energy

E = U + K

conserved

Mechanical energy is _________ when the sum of kinetic and potential energies remains constant

Work-energy theorem

relates the work performed by all forces acting on a body in a particular time interval to the change in energy at that time: W = ΔE

Conservation of energy

when there are no nonconservative forces (such as friction) acting on a system, the total mechanical energy remains constant: ΔE = ΔK + ΔU = 0