Acceleration calculator (and average velocity)
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Result
Calculate acceleration from a change in velocity over time, from the initial and final velocity and the distance travelled, or from the net force and the mass. A fourth mode finds the average speed of a trip made of several parts, and shows why it is not the mean of the speeds. Velocities can be entered in m/s, km/h or mph, and the acceleration is also given in g.
Step-by-step solution
Velocities in m/s
Acceleration = change of velocity ÷ time
Distance covered
Key formulas
- Velocity
- v = v0 + a·t
- Displacement
- s = v0·t + ½·a·t²
- Without time
- v² = v0² + 2·a·s
- Units
- 1 m/s = 3.6 km/h
How to calculate acceleration
- Convert the velocities to m/s: divide km/h by 3.6, or multiply mph by 0.447.
- From a time: a = (v − v₀)/t. A car going from 0 to 100 km/h (27.8 m/s) in 8 s accelerates at 3.47 m/s².
- From a distance: use v² = v₀² + 2·a·s, so a = (v² − v₀²)/(2s). The time then follows from t = 2s/(v₀ + v).
- From forces: Newton’s second law gives a = F/m, where F is the net force after subtracting friction and drag.
- For an average speed over several parts, divide the total distance by the total time.
Questions and answers
What does a negative acceleration mean?
The acceleration points opposite to the chosen positive direction. If the object moves in the positive direction, it is slowing down, which is often called deceleration.
Why is the average speed not the mean of the speeds?
Because the trip spends more time at the lower speeds. Driving 60 km at 60 km/h and 60 km at 30 km/h takes 3 h for 120 km, so the average is 40 km/h, not 45 km/h.
What is the difference between average speed and average velocity?
Average speed is the distance travelled divided by the time. Average velocity is the displacement, from start to end with direction, divided by the time. A round trip has a positive average speed but zero average velocity.
What is an acceleration of 1 g?
9.81 m/s², the acceleration of free fall. A fast road car reaches about 0.4 to 1 g when accelerating hard; fighter pilots can take about 9 g for short times.
Practise it yourself
Practise Kinematics
A calculator gives the answer. In the exam you need the method: practise it with new problems, hints and worked solutions.