Calculate Acceleration, Velocity Change, or Time | a = Δv / Δt | Physics Tool
Result
--
📝 Step-by-step solution
Select what to calculate and enter values
💡 Acceleration a in m/s² | Velocity change Δv in m/s | Time Δt in seconds | 1 g = 9.80665 m/s²
📖 What is Acceleration?
Acceleration is the rate of change of velocity with respect to time.
It is a vector quantity, meaning it has both magnitude and direction.
In SI units, acceleration is measured in metres per second squared (m/s²).
When an object speeds up, slows down, or changes direction, it is accelerating.
This calculator uses the fundamental kinematic formula for average acceleration:
a = Δv / Δt
Where:
• a = Acceleration (m/s²)
• Δv = Change in velocity (final − initial) in m/s
• Δt = Time interval (s)
🔁 Rearranged Formulas
Acceleration: a = Δv / Δt Velocity change: Δv = a × Δt Time: Δt = Δv / a
📝 Worked Example
Example: A Car Accelerating from 0 to 100 km/h in 8 Seconds
Given: Initial velocity v₁ = 0 m/s | Final velocity v₂ = 27.78 m/s | Time Δt = 8 s
Step 1: Convert 100 km/h to m/s → 100 ÷ 3.6 = 27.78 m/s Step 2: Δv = v₂ − v₁ = 27.78 − 0 = 27.78 m/s Step 3: a = Δv / Δt = 27.78 ÷ 8 ≈ 3.47 m/s²
Result: The car accelerates at approximately 3.47 m/s².
📊 Common Acceleration Values
Free fall (Earth): 9.81 m/s²
Free fall (Moon): 1.62 m/s²
Free fall (Mars): 3.72 m/s²
Passenger car (0–100 km/h in 10 s): ~2.8 m/s²
Sports car (0–100 km/h in 4 s): ~7 m/s²
Elevator (typical): 1–2 m/s²
Rocket launch: 20–40 m/s²
Braking car (emergency): −8 to −10 m/s²
⚠️ Limitations & Assumptions
📌 Important Notes
Calculates average acceleration over the given time interval.
Assumes uniform (constant) acceleration for the duration.
For non-uniform acceleration, instantaneous acceleration may differ.
Signs matter: negative acceleration means slowing down (deceleration) in the direction of motion.
Does not account for air resistance, friction, or relativistic effects.
📚 Sources & References
Authoritative Sources
OpenStax — University Physics, Volume 1
NIST — SI Units and Constants
Khan Academy — Acceleration and Kinematics
Halliday, Resnick, Walker — Fundamentals of Physics
❓ Frequently Asked Questions
What is the difference between acceleration and velocity?
Velocity is the rate of change of position (m/s).
Acceleration is the rate of change of velocity (m/s²).
An object can have zero velocity but non-zero acceleration (e.g., a ball at the top of its flight).
Can acceleration be negative?
Yes — negative acceleration (deceleration) means the object is slowing down
in the direction of motion, or accelerating in the opposite direction.
What is the standard acceleration due to gravity?
On Earth, the standard acceleration due to gravity is 9.80665 m/s²,
often rounded to 9.81 m/s² in physics problems.
How do I convert km/h to m/s?
Divide by 3.6. For example, 100 km/h ÷ 3.6 = 27.78 m/s.
This Acceleration Calculator is provided for informational and educational purposes only.
Results are based on the standard kinematic formula a = Δv / Δt and assume uniform acceleration.
Real-world motion may involve varying acceleration, air resistance, friction, or relativistic effects.
Always verify critical calculations with authoritative sources or a qualified professional.