MCAT Physics: Fluids, Circuits, Waves and Optics Formulas (University)

v=final velocity, v0=initial velocity, a=acceleration, t=time. Trap: deceleration means a is negative, not that v itself must be negative — watch sign convention.

Δx=displacement, v0=initial velocity, a=acceleration, t=time. Trap: students forget the v0t term when the object is already moving, not starting from rest.

Use when time is unknown. v=final velocity, v0=initial, a=acceleration, Δx=displacement. Trap: taking the square root gives ± v — pick the sign matching the direction of motion.

v0=launch speed, θ=launch angle, g=9.8 m/s². Worked example: v0=20 m/s, θ=45°, g=10 → R=400×1/10=40 m, matching the parabola shown.

F_net=net force, m=mass, a=acceleration, v=speed, r=radius. Trap: centripetal force isn't a new force type — it's whatever net force (tension, gravity, friction) points toward the center.

Trap: action-reaction pairs never cancel because they act on different bodies, not the same one — don't confuse with force balance on a single object.

μ=coefficient of friction, N=normal force. Trap: μs is always ≥ μk, so it takes more force to start motion than to maintain it.

F=force, d=displacement, θ=angle between them. Trap: holding a heavy object stationary does zero work even though it feels effortful.

m=mass, v=speed. Trap: only the NET work changes KE — individual forces can do work that cancels out, leaving KE unchanged.

m=mass, g=9.8 m/s², h=height above a reference level. Trap: the reference point is arbitrary; only ΔPE between two points has physical meaning.

W=work, t=time, F=force, v=velocity, θ=angle between F and v. Units: Watts = J/s. Trap: don't confuse power with work — power accounts for the rate.

p=momentum (vector), m=mass, v=velocity. Trap: direction matters — momentum is a vector, so components must be added/subtracted accordingly in collisions.

J=impulse, F=force, Δt=contact time, Δp=change in momentum. Trap: increasing Δt (airbags, bending knees) reduces the force needed for the same Δp.

Trap: students wrongly assume KE is conserved in every collision — momentum conservation is universal, KE conservation is not.

ρ=density, m=mass, V=volume. Trap: an object floats if its average density is less than the fluid's density, regardless of its total mass or size.

P=pressure (Pa=N/m²), F=force, A=area. Trap: pressure is a scalar that acts equally in all directions at a given point (Pascal's principle).

P0=pressure at surface, ρ=fluid density, g=9.8 m/s², h=depth. Trap: pressure depends only on depth and density, not container shape or total fluid volume.

ρ_fluid=fluid density, g=9.8 m/s², V_displaced=volume of fluid displaced. Trap: use the volume of fluid DISPLACED, not the object's total volume, for partially submerged objects.

A=cross-sectional area, v=flow speed, assumes incompressible fluid. Trap: flow speed increases where the pipe narrows — area and velocity are inversely related.

P=pressure, ρ=fluid density, v=speed, g=9.8, h=height. Trap: faster-moving fluid has LOWER pressure at the same height (explains lift, aspirators).

Q=flow rate, ΔP=pressure difference, r=radius, η=viscosity, L=length. Trap: flow rate scales with r⁴ — tiny changes in vessel radius cause huge changes in flow (key in physiology).

k=8.99×10⁹ N·m²/C², q1,q2=charges, r=distance. Trap: like charges repel, opposite charges attract — this is an inverse-square law just like gravity.

F=force on test charge, q=test charge, k=Coulomb's constant, Q=source charge, r=distance. Trap: field direction points away from positive source charges and toward negative ones, independent of the test charge's sign.

V=electric potential (scalar, can be negative), Q=source charge, r=distance, q=test charge. Trap: don't confuse potential V (property of the field) with potential energy PE (depends on the test charge placed in it).

V=voltage drop, I=current, R=resistance. Trap: V here is the drop ACROSS a resistor, not necessarily the full battery EMF if there's internal resistance or multiple elements.

P=power, I=current, V=voltage, R=resistance. Trap: pick the version that uses only the variables you're given to avoid unnecessary extra calculation steps.

Trap: adding a resistor in parallel always DECREASES total resistance (R_eq is less than the smallest individual resistor), opposite of the series case.

C=Q/V for each capacitor. Trap: capacitor combination rules are the OPPOSITE of resistor rules — series capacitors add as reciprocals, parallel capacitors add directly.

q=charge, v=speed, B=field, θ=angle to field, I=current, L=wire length. Trap: force is zero when motion/current is parallel or antiparallel to B (θ=0° or 180°); direction found via right-hand rule.

v=wave speed, f=frequency, λ=wavelength. Trap: wave speed is set by the medium, not by frequency — changing f changes λ inversely while v stays fixed.

f'=observed freq, f=source freq, v=speed of sound, v_o=observer speed, v_s=source speed. Trap: use the sign combination that increases f' when source and observer approach each other, decreases it when receding.

β=sound level in dB, I=intensity. Trap: the scale is logarithmic — a +10 dB increase means 10× the intensity, not 10× the perceived loudness or a linear jump.

n1,n2=refractive indices, θ1,θ2=angles from normal. Trap: total internal reflection only occurs going from a HIGHER index medium to a LOWER one, never the reverse.

f=focal length, do=object distance, di=image distance, hi/ho=image/object height. Trap: sign conventions matter — negative di means a virtual image, negative m means an inverted image.

ΔU=change in internal energy, Q=heat added to system, W=work done BY the system on surroundings. Trap: physics and chemistry texts sometimes flip the sign of W — always check which convention is used.

P=pressure, V=volume, n=moles, R=8.314 J/(mol·K) or 0.0821 L·atm/(mol·K), T=temperature. Trap: T must be in Kelvin, not Celsius, or the equation gives wrong results.

W=net work output, Qh=heat absorbed from hot reservoir, Qc=heat exhausted to cold reservoir. Trap: efficiency is always less than 100%, and Qc represents wasted heat, not useful output.

Trap: beta-PLUS decay (positron emission) decreases atomic number by 1, the opposite effect of beta-minus — don't confuse the two.

N(t)=amount remaining, N0=initial amount, t½=half-life. Trap: decay is exponential, not linear — the quantity approaches but mathematically never reaches exactly zero.