How to Calculate Acceleration
Master how to calculate acceleration using the formula a = Δv/Δt, with worked examples from physics and everyday motion. Understand uniform acceleration, deceleration, and free fall.
What is Acceleration?
Acceleration is the rate of change of velocity over time. Unlike speed, both velocity and acceleration are vector quantities — they have both magnitude and direction. An object accelerates whenever its speed changes, its direction changes, or both. Even a car turning at constant speed is accelerating (centripetal acceleration) because its direction is changing.
The Acceleration Formula
a = Δv ÷ Δt = (v_final − v_initial) ÷ (t_final − t_initial). The SI unit of acceleration is meters per second squared (m/s²). A car that accelerates from 0 to 27.8 m/s (0 to 100 km/h) in 8 seconds has an average acceleration of (27.8 − 0) ÷ 8 = 3.47 m/s².
Positive and Negative Acceleration
Positive acceleration means the object is speeding up in the chosen positive direction. Negative acceleration (deceleration) means it is slowing down or moving faster in the negative direction. A car braking from 30 m/s to 0 in 6 seconds has acceleration a = (0 − 30) ÷ 6 = −5 m/s². The braking force must be calculated separately using F = ma.
Uniform Acceleration Equations (SUVAT)
For constant (uniform) acceleration, a set of kinematic equations called SUVAT relate displacement (s), initial velocity (u), final velocity (v), acceleration (a), and time (t): v = u + at; s = ut + ½at²; v² = u² + 2as; s = ½(u+v)t. These allow you to solve any uniform acceleration problem when three of the five variables are known.
Free Fall and Gravitational Acceleration
Near Earth's surface, gravity accelerates all freely falling objects at g ≈ 9.81 m/s² downward (ignoring air resistance). An object dropped from rest reaches v = g × t after t seconds: after 3 seconds it is moving at 9.81 × 3 = 29.4 m/s. The distance fallen is s = ½ × 9.81 × t²: after 3 seconds it has fallen ½ × 9.81 × 9 = 44.1 m.
Centripetal Acceleration
An object moving in a circle of radius r at constant speed v experiences centripetal acceleration directed toward the center: a_c = v² ÷ r. A car turning through a curve of radius 50 m at 20 m/s experiences a_c = 20² ÷ 50 = 8 m/s² directed toward the center of the curve. The centripetal force required is F = m × a_c = m × v² ÷ r, provided by friction or a banked road surface.
Measuring Acceleration in Practice
Accelerometers in smartphones, aircraft, and automotive airbag systems directly measure acceleration in all three axes. In laboratory settings, acceleration is derived by measuring velocity at two points using photogates and dividing by the time interval. Graphically, acceleration equals the slope of a velocity-time (v-t) graph — a steeper slope means greater acceleration.
Try These Calculators
Put what you learned into practice with these free calculators.
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