📐 Displacement Calculator
Calculate displacement
How to Use This Calculator
Enter Initial Velocity
Input the initial velocity (v₀) in m/s. This is the object's velocity at the start of the time interval. Use 0 for objects starting from rest.
Enter Time
Enter the time duration (t) in seconds over which the motion occurs. This is the time interval during which displacement is measured.
Enter Acceleration
Input the acceleration (a) in m/s². Use positive for speeding up in the positive direction, negative for deceleration or reverse direction. For free fall, use 9.81 m/s².
Click Calculate
Press "Calculate" to find the displacement and final velocity using kinematic equations.
Formula
s = v₀t + ½at²
v = v₀ + at
Where:
- s = Displacement (m)
- v₀ = Initial velocity (m/s)
- v = Final velocity (m/s)
- a = Acceleration (m/s²)
- t = Time (s)
Example Calculation:
A car accelerates from 10 m/s with 2 m/s² for 5 seconds:
1. Displacement: s = (10 × 5) + (½ × 2 × 5²) = 50 + (½ × 2 × 25) = 50 + 25 = 75 m
2. Final velocity: v = 10 + (2 × 5) = 10 + 10 = 20 m/s
About Displacement Calculator
The Displacement Calculator uses kinematic equations to determine how far an object moves and its final velocity when you know its initial velocity, acceleration, and time. Displacement differs from distance - it's the straight-line change in position, which can be negative if the object moves backward.
Displacement vs. Distance
Displacement is a vector quantity measuring the change in position from start to finish (includes direction). Distance is a scalar measuring total path length traveled. For example, walking 10 m north then 10 m south gives 20 m distance but 0 m displacement.
Key Applications
- Physics Problems: Solve kinematics problems involving uniformly accelerated motion.
- Engineering: Calculate stopping distances for vehicles, design braking systems, and analyze motion control systems.
- Sports Science: Analyze athlete movements, sprint distances, and acceleration patterns.
- Vehicle Dynamics: Determine how far vehicles travel during acceleration or deceleration phases.
Understanding Acceleration
Acceleration can be positive (speeding up), negative (slowing down), or zero (constant velocity). The sign of acceleration combined with initial velocity determines whether displacement increases or decreases. For example, negative acceleration with positive velocity means the object is slowing down but still moving forward.
Frequently Asked Questions
What's the difference between displacement and distance?
Displacement is the straight-line change in position (a vector with direction), while distance is the total path length traveled (a scalar). If you go 10 m east then 10 m west, distance = 20 m, but displacement = 0 m.
Can displacement be negative?
Yes! Displacement is a vector, so it can be negative. Negative displacement means the object moved in the negative direction (backward, down, left, etc.) from your chosen reference point.
What if acceleration is zero?
With zero acceleration (constant velocity), the formula simplifies to s = v₀t. The object moves at constant speed, so displacement equals velocity times time.
How do I use this for free fall?
For objects dropped from rest (v₀ = 0) in free fall, set initial velocity to 0 and acceleration to 9.81 m/s² (or your local gravity). The formula becomes s = ½gt².
Does this work for non-constant acceleration?
This calculator assumes constant acceleration. For variable acceleration, you'd need calculus (integration) or numerical methods. The kinematic equations only apply when acceleration is uniform.
What units should I use?
Use SI units: meters (m) for displacement, meters per second (m/s) for velocity, meters per second squared (m/s²) for acceleration, and seconds (s) for time. The calculator will give results in these units.