# Displacement Calculator

Calculate displacement using s = v₀t + ½at². Find final velocity and average velocity from initial velocity, acceleration, and time.

## What this calculates

Displacement measures the change in position of an object under constant acceleration. Using the kinematic equation s = v₀t + ½at², this calculator determines how far an object travels, its final velocity, and its average velocity over a given time interval.

## Inputs

- **Initial Velocity (v₀)** (m/s) — Starting velocity of the object.
- **Acceleration (a)** (m/s²) — Constant acceleration applied to the object.
- **Time (t)** (s) — min 0 — Duration of motion.

## Outputs

- **Displacement** (m) — s = v₀t + ½at²
- **Final Velocity** (m/s) — v = v₀ + at
- **Average Velocity** (m/s) — v_avg = (v₀ + v) / 2

## Details

The displacement formula s = v₀t + ½at² is one of the four fundamental kinematic equations for uniformly accelerated motion. It combines the distance traveled due to initial velocity (v₀t) with the additional distance from acceleration (½at²).

The final velocity v = v₀ + at tells you how fast the object is moving at the end of the time period. The average velocity is simply the mean of initial and final velocities, which for constant acceleration equals (v₀ + v) / 2. This also equals the total displacement divided by the total time.

These equations assume constant (uniform) acceleration. They apply to many real-world scenarios: a car accelerating from a stop light, an object in free fall (where a = g = 9.81 m/s²), or a spacecraft firing its engines. For non-uniform acceleration, calculus-based methods are required.

## Frequently Asked Questions

**Q: What is the difference between displacement and distance?**

A: Displacement is a vector measuring the straight-line change in position from start to end, including direction. Distance is a scalar measuring the total path length traveled. An object that returns to its starting point has zero displacement but nonzero distance.

**Q: Can displacement be negative?**

A: Yes. Negative displacement means the object has moved in the negative direction (e.g., backward or downward depending on your coordinate system). For example, a ball thrown upward with deceleration will eventually have negative displacement as it falls below its starting point.

**Q: What are the kinematic equations?**

A: The four kinematic equations for constant acceleration are: (1) v = v₀ + at, (2) s = v₀t + ½at², (3) v² = v₀² + 2as, and (4) s = ½(v₀ + v)t. Each relates displacement, velocity, acceleration, and time in different combinations.

**Q: Does this calculator work for free fall?**

A: Yes. For free fall, set initial velocity to the object's launch speed (0 if dropped from rest) and acceleration to 9.81 m/s² (or -9.81 m/s² for upward positive convention). The calculator will give the displacement and final velocity.

**Q: What if acceleration is zero?**

A: With zero acceleration, the object moves at constant velocity. The displacement simplifies to s = v₀t, and final velocity equals initial velocity. This is uniform motion.

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Source: https://vastcalc.com/calculators/physics/displacement
Category: Physics
Last updated: 2026-04-21