Formula & Mathematical Principles
In physics, calculating mass directly from force and speed requires considering time, as force represents the rate of change of momentum over time ($F = \frac{\Delta p}{\Delta t}$).
1. Classical Mechanics (Newtonian)
Under Newton's Second Law of Motion ($F = ma$), acceleration is defined as speed divided by time ($a = \frac{v}{t}$) assuming an initial state at rest. Substituting this gives the impulse-momentum theorem:
F · t = m · v ⇒ m = (F · t) / v
- $m$: Mass in kilograms (kg)
- $F$: Constant Force in Newtons (N)
- $t$: Time duration in seconds (s)
- $v$: Final Speed in meters per second (m/s)
2. Relativistic Mechanics (Einsteinian)
At velocities approaching the speed of light ($c \approx 3 \times 10^8 \text{ m/s}$), relativistic momentum must be considered using the Lorentz factor ($\gamma$):
m = (F · t) / (γ · v), where γ = 1 / √(1 - v²/c²)
This accounts for relativistic effects where mass-energy equivalence limits acceleration as speed nears $c$.