Acceleration by Distance
Calculator and formulas for calculating acceleration by distance
Acceleration Calculator
Kinematics with constant acceleration
Calculates the relationship between acceleration (a), initial velocity (v₀), final velocity (v) and distance (s).
Example Calculation
Example: Car acceleration
Problem:
A car accelerates from 0 km/h to 100 km/h and covers a distance of 200 m. What is the average acceleration?
Given:
- Initial velocity v₀ = 0 km/h = 0 m/s
- Final velocity v = 100 km/h = 27.78 m/s
- Distance s = 200 m
- Find: Acceleration a
Solution:
1. Conversion km/h → m/s:
2. Calculate acceleration:
Practical applications
Kinematic fundamentals
Important: These formulas only apply for constant acceleration. In reality, acceleration often varies, so these are usually average values over the considered distance.
Formulas for acceleration
These formulas are based on the kinematic equations for uniformly accelerated motion. They connect acceleration, velocities and distance traveled.
Calculate acceleration
Calculation of acceleration from initial, final velocity and distance.
v = Final velocity [m/s]
v₀ = Initial velocity [m/s]
s = Distance [m]
Calculate initial velocity
Calculation of initial velocity with known final velocity.
Calculate final velocity
Calculation of final velocity after a certain distance.
Calculate distance
Calculation of distance traveled with known velocities.
Important notes
- These formulas only apply for constant acceleration
- For braking processes, acceleration is negative (deceleration)
- Units must be used consistently (SI units recommended)
- The formulas are based on the conservation of energy and kinematics
Detailed description of acceleration
Physical Fundamentals
Acceleration describes the change in velocity per unit of time. With constant acceleration, we can use the kinematic equations to calculate relationships between velocity, time, distance and acceleration.
These special formulas use energy considerations, since kinetic energy is proportional to the square of velocity.
Usage Instructions
Select with the radio buttons which quantity should be calculated. Enter the known values and choose the appropriate units.
Application Areas
Automotive Engineering
Acceleration testing, braking distance calculation, performance diagrams. Foundation for vehicle dynamics and safety systems.
Traffic Safety
Accident reconstruction, speed analysis, traffic planning. Important for forensic investigations.
Mechanical Engineering
Conveyor systems, elevators, production lines, robotics. Dimensioning of drives and safety systems.
Understanding acceleration
Acceleration is present everywhere in our daily life. The most important concepts and their practical significance:
Positive acceleration
a > 0
Velocity increases
Car when starting
Negative acceleration
a < 0 (deceleration)
Velocity decreases
Car when braking
Uniform motion
a = 0
Velocity constant
Car at constant speed
Example: A sports car with 400 HP can accelerate from 0 to 100 km/h in about 4 seconds. This corresponds to an acceleration of about 7 m/s², almost 0.7 times the acceleration due to gravity!
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