Equations of Motion with Constant Acceleration
Interactive Visualization of Kinematic Equations
Kinematic Equations (Constant Acceleration)
\[ \begin{aligned}
&1.\ v = v_0 + at \\
&2.\ x = x_0 + v_0t + \frac{1}{2}at^2 \\
&3.\ v^2 = v_0^2 + 2a(x - x_0)
\end{aligned} \]
Current Motion State
Time: 0.0 s
Velocity: 5.0 m/s
Position: 0.0 m
Simulation Parameters
Initial Velocity (v₀): 5.0 m/s
Acceleration (a): 2.0 m/s²
Initial Position (x₀): 0.0 m
Derivation of First Equation (v = v₀ + at)
By definition of acceleration:
\[ a = \frac{dv}{dt} \]
Separate variables for integration:
\[ dv = a \, dt \]
Integrate both sides (from v₀ to v and 0 to t):
\[ \int_{v_0}^{v} dv = \int_{0}^{t} a \, dt \]
Since acceleration is constant:
\[ v - v_0 = at \]
Final velocity equation:
\[ v = v_0 + at \]
