Acceleration Calculator - Calculate Physics Motion & Kinematic Equations
Free acceleration calculator. Calculate acceleration, velocity, distance, and force using kinematic equations with step-by-step solutions. Our calculator uses Newton's laws of motion and kinematic equations to determine all motion parameters from any given inputs.
Last updated: October 19, 2025
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5 m/s²
50 m/s
250 m
0 m/s
10 s
50 N
10 kg
Acceleration Formula
a = (v_f - v_0) / t
Velocity Formula
v_f = v_0 + at
Distance Formula
d = v_0t + ½at²
Force Formula
F = ma
Key Relationships:
- • Acceleration = Change in velocity / Time
- • Final velocity = Initial velocity + (Acceleration × Time)
- • Distance = Initial velocity × Time + ½ × Acceleration × Time²
- • Force = Mass × Acceleration (Newton's Second Law)
Acceleration Calculator Types & Features
Formula used
a = (v_f - v_0) / t
Calculates acceleration from change in velocity over time
Formula used
a = (v_f² - v_0²) / (2d)
Calculates acceleration from velocity and distance
Formula used
a = F / m
Uses Newton's Second Law to find acceleration
Formula used
a = Δv / Δt
Calculates acceleration from velocity change over time
Equations used
v_f = v_0 + at
Applies all kinematic equations for motion analysis
Analysis includes
v, a, d, t, F
Comprehensive motion parameter calculations
Quick Example Result
For acceleration = 5 m/s², time = 10 s, initial velocity = 0 m/s:
Final Velocity
50 m/s
Distance
250 m
Force
50 N
How Our Acceleration Calculator Works
Our acceleration calculator uses the fundamental principles of kinematics and Newton's laws of motion to calculate all motion parameters from any given inputs. The calculation applies kinematic equations and force relationships to determine acceleration, velocity, distance, and force.
The Kinematic Equations
v_f = v_0 + atd = v_0t + ½at²v_f² = v_0² + 2adF = maThese equations form the foundation of classical mechanics and allow calculation of all motion parameters from any combination of known values. They apply to constant acceleration motion.
Shows the relationships between velocity, acceleration, distance, and time
Mathematical Foundation
Acceleration is the fundamental concept in kinematics, representing the rate of change of velocity. It's directly related to force through Newton's Second Law and forms the basis for understanding all motion in classical physics.
- Acceleration is the derivative of velocity with respect to time
- Constant acceleration leads to linear velocity change
- Force is proportional to acceleration (F = ma)
- Kinematic equations assume constant acceleration
- Acceleration can be positive (speeding up) or negative (slowing down)
- Gravitational acceleration is approximately 9.8 m/s² on Earth
Sources & References
- Physics for Scientists and Engineers - Serway & JewettStandard reference for kinematic equations and motion analysis
- Fundamentals of Physics - Halliday, Resnick, WalkerComprehensive coverage of Newton's laws and kinematics
- Khan Academy - Kinematics and MotionEducational resources for understanding acceleration and motion
Need help with other physics calculations? Check out our free fall calculator and momentum calculator.
Get Custom Calculator for Your PlatformAcceleration Calculator Examples
Given Information:
- Initial velocity: 0 m/s (at rest)
- Acceleration: 3 m/s²
- Time: 8 seconds
- Mass: 1200 kg
Calculation Steps:
- Final velocity = 0 + (3 × 8) = 24 m/s
- Distance = (0 × 8) + ½(3 × 8²) = 96 m
- Force = 1200 × 3 = 3600 N
- All units in SI system
Result: Final velocity = 24 m/s, Distance = 96 m, Force = 3600 N
The car reaches 24 m/s (86.4 km/h) in 8 seconds, traveling 96 meters.
Free Fall Example
Object dropped from height
a = 9.8 m/s² (gravity), v_f = gt
Braking Example
Car decelerating to stop
Negative acceleration (deceleration)
Frequently Asked Questions
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