Acceleration Velocity Time Distance Calculator

Kinematic Equations:

\[ v = u + at \] \[ s = ut + \frac{1}{2}at^2 \] \[ v^2 = u^2 + 2as \] \[ s = \frac{(u + v)}{2}t \]

Initial Velocity (u):

m/s

Final Velocity (v):

m/s

Acceleration (a):

m/s²

Time (t):

Distance (s):

Calculation Results:

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1. What are Kinematic Equations?

Kinematic equations describe the motion of objects without considering the forces that cause the motion. These equations relate five key variables: initial velocity (u), final velocity (v), acceleration (a), time (t), and displacement (s).

2. How Does the Calculator Work?

The calculator uses the four standard kinematic equations:

\[ v = u + at \] \[ s = ut + \frac{1}{2}at^2 \] \[ v^2 = u^2 + 2as \] \[ s = \frac{(u + v)}{2}t \]

Where:

\( u \) — Initial velocity (m/s)
\( v \) — Final velocity (m/s)
\( a \) — Acceleration (m/s²)
\( t \) — Time (s)
\( s \) — Displacement (m)

Explanation: You need to provide exactly three known values, and the calculator will solve for the remaining two unknown values using the appropriate equations.

3. Applications of Kinematic Equations

Details: Kinematic equations are fundamental in physics and engineering for solving motion problems. They're used in designing vehicles, analyzing sports movements, predicting projectile trajectories, and understanding celestial mechanics.

4. Using the Calculator

Tips: Enter exactly three known values and leave the other two fields empty. The calculator will automatically compute the missing values. All values should use standard SI units (meters, seconds, m/s, m/s²).

5. Frequently Asked Questions (FAQ)

Q1: What if acceleration is zero?
A: When acceleration is zero, the equations simplify to constant velocity motion: v = u and s = ut.

Q2: Can these equations handle deceleration?
A: Yes, deceleration is simply negative acceleration. Enter a negative value for acceleration when an object is slowing down.

Q3: Are these equations valid for all types of motion?
A: These equations are valid only for motion with constant acceleration in a straight line. They don't apply to circular motion or motion with changing acceleration.

Q4: What's the difference between distance and displacement?
A: Distance is the total path length traveled, while displacement is the straight-line distance between start and end points with direction. These equations calculate displacement.

Q5: Can I use different units?
A: The calculator expects SI units. If you have different units (like km/h or miles), convert them to m/s before entering the values.