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Average vs instantaneous acceleration
Intermediate
Compare Δv/Δt over an interval with the derivative at a moment.
Average acceleration is Δv/Δt over an interval; instantaneous acceleration is the slope of the v–t graph at one moment. They coincide only if acceleration is constant.
Velocity going from 0 to 10 m/s in 5 s gives an average of 2 m/s², even if the acceleration was 4 m/s² at first and 0 later.
Don't use the constant-acceleration equations with an average of varying acceleration.
In more detail
Average acceleration is the change in velocity divided by the time interval, while instantaneous acceleration is the derivative of velocity at a moment. They differ when acceleration changes over time.
Real-world uses
- Car tests quote average acceleration over a standard speed range.
- Sensors measure instantaneous acceleration in phones and vehicles.
- A car's average acceleration over a 10-second run from 0 to 30 m/s is 3 m/s², while its instantaneous acceleration at a given moment may be quite different.
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Frequently asked questions
Which one describes a crash best?
Instantaneous acceleration near the impact, since it captures the peak forces.
Can average acceleration be zero when instantaneous is not?
Yes, if the acceleration changes sign over the interval.
Can average and instantaneous acceleration be the same?
Yes, for constant acceleration, where every moment has the same value as the average over any interval.
Related topics in Kinematics
Frames: inertial vs non-inertial · Coriolis and fictitious motion · Chase and meeting problems