Kinematics Calculator: Velocity, Acceleration, a...

Understanding 1D Kinematics

Kinematics is the branch of classical mechanics that describes the motion of points, bodies, and systems of bodies without considering the mass or the forces that caused the motion. If you need to calculate exactly where a car, projectile, or falling object will be at a specific moment in time, kinematics is the toolkit you use.

🚀 Kinematics Solver

Stop doing algebraic algebra manually. Input your knowns and let our tool find the unknowns.

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📏 The Four Great Equations of Motion

Assuming constant acceleration, the four primary formulas are:

1. v = u + at

2. s = ut + ½at²

3. v² = u² + 2as

4. s = ½(u + v)t

Where s = displacement, u = initial velocity, v = final velocity, a = acceleration, and t = time. For video tutorials, Khan Academy's 1D Motion guide is excellent.

🏎️ Highway Acceleration Example

A car is waiting at a red light (u = 0). When green turns, it accelerates at a constant rate of 3 m/s² for 5 seconds. How far does it travel?

Using the equation s = ut + ½at²:
s = (0 × 5) + ½(3)(5)²
s = 0 + 1.5(25) = 37.5 meters

Our calculator spots which of the 4 equations to use automatically based on your empty variables.

❓ FAQ

What is the difference between speed and velocity?

Speed is a scalar quantity (just a magnitude, like 60 mph). Velocity is a vector quantity (magnitude and direction, like 60 mph North).

How does gravity apply here?

When an object is in freefall on Earth, "a" (acceleration) is swapped for "g" (gravity) which is uniformly 9.8 m/s² directed downwards. You insert -9.8 for "a" into the calculator.