Acceleration by Time
Calculator and formulas for calculating acceleration by time
Acceleration & Time Calculator
Time-dependent acceleration
Calculates the relationship between acceleration (a), initial velocity (v₀), final velocity (v) and time (t).
Example Calculation
Example: Sports car sprint
Problem:
A sports car accelerates from 0 km/h to 100 km/h in 3.2 seconds. 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
- Time t = 3.2 s
- Find: Acceleration a
Solution:
1. Conversion km/h → m/s:
2. Calculate acceleration:
Meaning: This corresponds to about 88% of Earth's gravity - a very sporty value!
Typical acceleration values
Basic kinematics
Definition: Acceleration is the change in velocity per unit of time. With constant acceleration, this change occurs uniformly. Negative values mean deceleration (braking).
Formulas for time-dependent acceleration
These formulas are based on the definition of acceleration as velocity change per time. They are the foundation of classical kinematics with constant acceleration.
Calculate acceleration
Basic formula of kinematics: velocity change per time.
v = Final velocity [m/s]
v₀ = Initial velocity [m/s]
t = Time [s]
Calculate initial velocity
Rearrangement for the initial velocity.
Calculate final velocity
Calculation of velocity after a certain time.
Calculate time
Required time for a certain velocity change.
Important conversions
1 m/s = 3.6 km/h
1 km/h = 0.278 m/s
1 min = 60 s
1 h = 3600 s
Earth's gravity: 9.81 m/s²
Typical car: 2-8 m/s²
Detailed description of time-dependent acceleration
Physical Fundamentals
Acceleration is defined as the change in velocity per unit of time. In contrast to distance-dependent acceleration, we consider here the linear temporal development of velocity with constant acceleration.
These formulas are the foundation of classical mechanics and describe uniformly accelerated motions, as they occur in many technical applications.
Usage Instructions
Select with the radio buttons which quantity should be calculated. Enter the known values and pay attention to the correct unit selection.
Application Areas
Automotive Engineering
Performance diagrams, sprint times, ride comfort evaluation. Basis for the development of drive systems.
Traffic Safety
Braking time calculations, traffic flow analyses, traffic light timing. Critical for safety system design.
Automation Technology
Servo drives, robotics, production systems. Precise motion control and timing optimization.
Understanding time-velocity relationships
The linear relationship between time and velocity with constant acceleration enables precise predictions and controls:
Starting
v₀ = 0, a > 0
Velocity increases linearly
v = a × t
Braking
a < 0 (deceleration)
Velocity decreases linearly
Until standstill
Uniform motion
a = 0
Velocity constant
v = v₀ (unchanged)
Practical example: A Tesla Model S can accelerate from 0 to 100 km/h in 2.1 seconds. This corresponds to an acceleration of about 13.2 m/s² - more than Earth's gravity!
Graphical representation
With constant acceleration, characteristic diagrams emerge:
Velocity-time diagram
Shows a straight line with slope a.
y-intercept = v₀
Slope = acceleration
Distance-time diagram
Shows a parabola.
s = v₀t + ½at²
Curvature shows acceleration
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