The fastest way to get comfortable with acceleration is to solve a few problems. Each acceleration formula example below starts from a real situation, picks the right equation, and works through the numbers so you can follow the method on your own problems.

The acceleration formulas you need

• From speeds and time: a = (v − u) ÷ t
• From speeds and distance: a = (v² − u²) ÷ (2s)
• From distance and time, starting at rest: a = 2s ÷ t²
• From force and mass: a = F ÷ m

u is the starting velocity, v the final velocity, t the time, s the distance, F the net force, and m the mass. Use metres, seconds, and kilograms throughout. The acceleration calculator solves the first form instantly.

Example 1: a car from 0 to 100 km/h

A car goes from rest to 100 km/h in 8 seconds. What is its average acceleration?

1. Convert to m/s: 100 ÷ 3.6 = 27.78 m/s.
2. a = (27.78 − 0) ÷ 8 = 3.47 m/s².

That is about a third of the acceleration due to gravity.

Example 2: braking (negative acceleration)

A cyclist at 12 m/s brakes to a stop in 4 seconds.

a = (0 − 12) ÷ 4 = −3 m/s². The minus sign shows deceleration: the speed drops by 3 m/s every second.

Example 3: speed change over a distance

A car speeds up from 10 m/s to 30 m/s over 200 m. No time is given, so use the distance form.

a = (30² − 10²) ÷ (2 × 200) = (900 − 100) ÷ 400 = 2 m/s².

Example 4: from rest, distance and time known

A sled starts from rest and covers 50 m in 5 seconds at steady acceleration.

From s = ½ a t², a = 2s ÷ t² = 2 × 50 ÷ 25 = 4 m/s². Its speed at 5 seconds is 4 × 5 = 20 m/s.

The speed distance time calculator checks the average speed of 10 m/s over that run.

Example 5: acceleration from force and mass

A net force of 1,500 N pushes a 1,200 kg car.

a = F ÷ m = 1,500 ÷ 1,200 = 1.25 m/s². Doubling the force doubles the acceleration; doubling the mass halves it.

Example 6: free fall

A stone is dropped from rest. Ignoring air drag, it accelerates at g = 9.81 m/s². After 3 seconds:

• Speed: v = 9.81 × 3 = 29.43 m/s
• Distance fallen: s = ½ × 9.81 × 3² = 44.1 m

The free fall calculator works out the speed and distance for any drop height or time.

Acceleration formula examples at a glance

Example	Formula used	Acceleration
Car 0 to 100 km/h in 8 s	(v − u) ÷ t	3.47 m/s²
Cyclist braking	(v − u) ÷ t	−3 m/s²
10 to 30 m/s over 200 m	(v² − u²) ÷ 2s	2 m/s²
Sled, 50 m in 5 s	2s ÷ t²	4 m/s²
1,500 N on 1,200 kg	F ÷ m	1.25 m/s²
Free fall	g	9.81 m/s²

How to pick the right formula

1. List what you know: speeds, time, distance, force, mass.
2. Choose the equation that uses only those values plus the acceleration.
3. Convert every unit to metres, seconds, and kilograms before you substitute.
4. Check the sign: speeding up is positive, slowing down is negative in the direction of motion.

To see these problems as lines and curves, read the guide to constant acceleration graphs.

Common mistakes

• Leaving speed in km/h. Divide by 3.6 to get m/s.
• Dropping the minus sign. A braking problem has a negative acceleration.
• Using a = 2s ÷ t² with a moving start. That shortcut only holds when the object starts from rest.

Quick reference

a = (v − u) ÷ t, a = (v² − u²) ÷ 2s, a = 2s ÷ t² from rest, a = F ÷ m. Solve your own problem with an online calculator from CalculateGuide.