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Velocity squared calculator

GCSEA-level Motion

Links final velocity, initial velocity, acceleration and displacement when time is not given.

v2 = u2 + 2a s

This free calculator is for GCSE and A-level physics. Choose the quantity you want to find, enter the other values with their units, and it shows the working in the layout used in exams, with the answer to the number of significant figures you choose. The values shown are an example. Change them to your own.

Quantity to find

8.72 m/s
m/s²

Working

  1. Write the equation
    v2 = u2 + 2a s
  2. Rearrange to make v the subject
    v = √(u2 + 2a s)
  3. Substitute the values
    v = √(42 + 2 × 3 × 10)
  4. Calculate
    v = 8.7178 m/s
  5. Give the answer to 3 significant figures
    v = 8.72 m/s

Worked example

Find v, the final velocity. Given: initial velocity u = 4.00 m/s; acceleration a = 3.00 m/s²; displacement s = 10.0 m.

  1. Write the equation
    v2 = u2 + 2a s
  2. Rearrange to make v the subject
    v = √(u2 + 2a s)
  3. Substitute the values
    v = √(42 + 2 × 3 × 10)
  4. Calculate
    v = 8.7178 m/s
  5. Give the answer to 3 significant figures
    v = 8.72 m/s

Symbols and units

SymbolQuantitySI unit
vFinal velocitym/s
uInitial velocitym/s
aAccelerationm/s²
sDisplacementm

Velocity squared: rearranged

  • To find final velocity: v = √(u2 + 2a s)
  • To find initial velocity: u = √(v2 − 2a s)
  • To find acceleration: a = (v2 − u2) / (2s)
  • To find displacement: s = (v2 − u2) / (2a)

Exam tip

A square root gives a positive value. Decide the direction from the situation, for example a ball moving upwards or downwards.

Common questions

What is the formula for velocity squared?

The equation is v² = u² + 2a s, where v is the final velocity (m/s); u is the initial velocity (m/s); a is the acceleration (m/s²); s is the displacement (m).

What units should I use for velocity squared?

In SI units: final velocity in m/s, initial velocity in m/s, acceleration in m/s², displacement in m. The calculator also accepts common alternatives such as kilometres, grams or minutes, and converts them for you.

How do I rearrange v² = u² + 2a s?

Rearranging gives these forms: to find final velocity: v = √(u² + 2a s). to find initial velocity: u = √(v² − 2a s). to find acceleration: a = (v² − u²) / (2s). to find displacement: s = (v² − u²) / (2a).

Practise velocity squared questions

Press the button for a question with random numbers. Work it out on paper first, then type your answer.

Related

More motion equations: Speed, distance and time, Acceleration, Final velocity, Displacement under constant acceleration, Displacement from average velocity, Momentum, Force and change in momentum, Centripetal force. See the full list on the physics equation calculator page.