Kinematic Equation Solver

Kinematic Equation Solver solves for a missing variable in one-dimensional motion with constant acceleration, using initial velocity, final velocity, acceleration, displacement, and time.

Enter known values (leave the unknown field blank):

Initial Velocity \\( v_0 \\) (m/s, e.g., 0):

Final Velocity \\( v \\) (m/s, e.g., 10):

Acceleration \\( a \\) (m/s², e.g., 2):

Displacement \\( \Delta x \\) (m, e.g., 20):

Time \\( t \\) (s, e.g., 5):

Methodology Used in Kinematic Equation Solver

The calculator uses the following kinematic equations, selecting the one that matches the known variables:

1. \\( v = v_0 + a t \\)

2. \\( \Delta x = v_0 t + \frac{1}{2} a t^2 \\)

3. \\( v^2 = v_0^2 + 2 a \Delta x \\)

4. \\( \Delta x = \frac{v + v_0}{2} t \\)

Where:

\\( v_0 \\): Initial velocity (m/s)
\\( v \\): Final velocity (m/s)
\\( a \\): Acceleration (m/s²)
\\( \Delta x \\): Displacement (m)
\\( t \\): Time (s)

The solver identifies the missing variable, selects the appropriate equation, and solves algebraically, showing each step.

Example Calculation

Sample Input

Initial Velocity = 0 m/s, Acceleration = 2 m/s², Time = 5 s, Displacement = 25 m, Final Velocity = ?

Step 1: Identify knowns: \\( v_0 = 0 \\), \\( a = 2 \\), \\( t = 5 \\), \\( \Delta x = 25 \\), solve for \\( v \\).

Step 2: Select equation with \\( v_0 \\), \\( a \\), \\( t \\), and \\( v \\):

\\[ v = v_0 + a t \\]

Step 3: Substitute values:

\\[ v = 0 + 2 \cdot 5 \\] \\[ v = 10 \, \text{m/s} \\]

Step 4: Verify with another equation (e.g., equation 2):

\\[ \Delta x = v_0 t + \frac{1}{2} a t^2 \\] \\[ 25 = 0 \cdot 5 + \frac{1}{2} \cdot 2 \cdot 5^2 \\] \\[ 25 = 0 + \frac{1}{2} \cdot 2 \cdot 25 = 25 \\]

Result: Final Velocity = 10 m/s.