Acceleration Calculator
Calculate acceleration from initial velocity, final velocity, and time.
Also computes distance traveled during acceleration.
Acceleration is the rate at which an object’s velocity changes over time. Newton’s Second Law of Motion connects acceleration, force, and mass — one of the most powerful equations in all of physics.
Newton’s Second Law: F = m × a Which rearranges to: a = F ÷ m (acceleration equals net force divided by mass) m = F ÷ a (mass equals force divided by acceleration)
Kinematic acceleration formula: a = (v_f − v_i) ÷ t where v_f = final velocity, v_i = initial velocity, t = time elapsed.
Units:
- Force (F) in Newtons (N) = kg·m/s²
- Mass (m) in kilograms (kg)
- Acceleration (a) in meters per second squared (m/s²)
- In imperial: Force in pounds-force (lbf), mass in slugs, acceleration in ft/s²
Key reference accelerations:
- Earth’s gravity (g) = 9.81 m/s² (32.2 ft/s²)
- Typical car 0–60 mph (0–97 km/h) = ~5–8 m/s² for performance cars
- Space Shuttle launch ≈ 29 m/s² (~3g) at liftoff
- Fighter jet maximum ≈ 88 m/s² (~9g) in a tight turn
- Bullet from rifle ≈ 1,000,000 m/s² in barrel (extremely brief)
- Human unconsciousness threshold ≈ 50–100 m/s² sustained (5–10g)
Worked example 1 — Newton’s Second Law: A 1,200 kg car engine applies 4,800 N of net force. a = F ÷ m = 4,800 ÷ 1,200 = 4 m/s² From rest (v_i = 0), after 5 seconds: v_f = 0 + 4 × 5 = 20 m/s (72 km/h or 45 mph)
Worked example 2 — kinematic: A ball rolling at 2 m/s decelerates to a stop in 4 seconds. a = (0 − 2) ÷ 4 = −0.5 m/s² (deceleration / negative acceleration) Braking force on a 0.5 kg ball = 0.5 × 0.5 = 0.25 N
Gravity on other planets (m/s²):
- Moon: 1.62 | Mars: 3.72 | Venus: 8.87 | Jupiter: 24.8 | Saturn: 10.4
The same force applied to a smaller mass produces greater acceleration — why a baseball bat accelerates faster than a car when pushed with the same force.