Acceleration Calculator
Calculate acceleration, distance, and average velocity from velocity and time
Table of Contents
How to Use
- Select your unit system (metric or imperial)
- Enter the initial velocity
- Enter the final velocity
- Enter the time period
- Click calculate to see acceleration, distance, and average velocity
What is Acceleration?
Acceleration is the rate at which velocity changes over time. It's a fundamental concept in physics that describes how quickly an object speeds up, slows down, or changes direction.
The basic formula for acceleration is: a = (v_f - v_i) / t, where a is acceleration, v_f is final velocity, v_i is initial velocity, and t is time.
Acceleration Formula
The acceleration calculator uses three fundamental formulas from kinematics:
- Acceleration: a = (v_f - v_i) / t
- Average Velocity: v_avg = (v_i + v_f) / 2
- Distance Traveled: d = v_avg × t or d = v_i × t + 0.5 × a × t²
Where: a = acceleration, v_f = final velocity, v_i = initial velocity, t = time, d = distance, v_avg = average velocity
Types of Acceleration
| Type | Description | Acceleration Value |
|---|---|---|
| Positive Acceleration | Object is speeding up | a > 0 |
| Negative Acceleration (Deceleration) | Object is slowing down | a < 0 |
| Zero Acceleration | Object moves at constant velocity | a = 0 |
Real-World Examples
- Car accelerating from 0 to 60 mph: Positive acceleration
- Car braking from 60 mph to 0: Negative acceleration (deceleration)
- Gravity on Earth: 9.8 m/s² (32.2 ft/s²) downward acceleration
- Rocket launch: Very high positive acceleration
- Free-falling object: Constant acceleration due to gravity
- Train cruising at constant speed: Zero acceleration
Applications of Acceleration
Understanding acceleration is crucial in many fields:
- Automotive engineering: Designing vehicle performance and safety systems
- Aerospace: Calculating rocket trajectories and spacecraft motion
- Sports science: Analyzing athlete performance and motion
- Accident reconstruction: Determining speeds and forces in collisions
- Roller coaster design: Ensuring rider safety and comfort
- Physics education: Teaching fundamental concepts of motion
Frequently Asked Questions
- What is the difference between acceleration and velocity?
- Velocity is the rate of change of position (how fast you're moving), while acceleration is the rate of change of velocity (how fast your speed is changing). You can have high velocity but zero acceleration if you're moving at a constant speed.
- Can acceleration be negative?
- Yes, negative acceleration (also called deceleration) occurs when an object is slowing down. For example, when you apply brakes to a car, it experiences negative acceleration.
- What is the acceleration due to gravity?
- On Earth, gravity causes objects to accelerate downward at approximately 9.8 m/s² (or 32.2 ft/s²). This means that in free fall, an object's velocity increases by 9.8 m/s every second.
- How do I convert between metric and imperial units?
- For acceleration: 1 m/s² = 3.28 ft/s². For velocity: 1 m/s = 2.237 mph. The calculator handles these conversions automatically when you select your preferred unit system.