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    Force and Momentum Change Calculator (F = mΔv/Δt)

    GCSE PhysicsAQAEdexcelOCRHigher tier, GCSE Physics only

    Find the force, mass, change in velocity or time using F = m × Δv ÷ Δt, the rate of change of momentum.

    Quick answer

    Force = change in momentum ÷ time = m × Δv ÷ Δt. For example, a 0.45 kg ball sped up by 20 m/s in 0.050 s needs a force of 0.45 × 20 ÷ 0.050 = 180 N. A longer time gives a smaller force.

    By Engr. Mehmood Kakar · Updated

    F = m × Δv ÷ Δt
    Find:

    Use the size of the change. If an object bounces back, add the two speeds.

    Simulation

    Longer stopping time, smaller force

    A car stops in a crash. Change the mass, the change in velocity and the time the crash takes: crumple zones make the time longer and the force smaller.

    1000 kg
    15 m/s
    0.1 s

    Force = rate of change of momentum. Crumple zones, airbags and seat belts all increase the time taken to stop, which reduces the force on the people inside.

    Put these numbers in the calculator above

    How to use F = mΔv/Δt

    A force changes an object's momentum. The bigger the change in momentum, and the shorter the time it happens in, the bigger the force:

    force = mass × change in velocity ÷ time taken

    • F is force in newtons (N)
    • m is mass in kg; m Δv is the change in momentum in kg m/s
    • Δv is the change in velocity in m/s and Δt is the time in seconds

    A 0.45 kg football kicked from rest to 20 m/s in 50 ms (0.050 s) feels a force of 0.45 × 20 ÷ 0.050 = 180 N.

    This explains many safety features. Airbags, seat belts, crumple zones and cycle helmets all increase the time taken for your momentum to change in a collision. A longer time means a smaller force on you, so less injury.

    Common mistakes that cost marks

    1. Leaving time in milliseconds. 50 ms is 0.050 s.
    2. Using final velocity instead of the change. Δv = final − initial.
    3. Bouncing objects. If a ball rebounds, the change in velocity is the two speeds added together.
    4. Thinking safety features reduce the momentum change. They increase the time, which reduces the force.

    Practice questions

    Try each one on paper first, then reveal the worked answer.

    Q1A 0.45 kg football is kicked from rest to 20 m/s. The kick lasts 50 ms. Calculate the average force.[3 marks]
    1. Convert: Δt = 50 ÷ 1000 = 0.050 s
    2. F = m × Δv ÷ Δt
    3. F = 0.45 × 20 ÷ 0.050
    4. F = 180 N
    Q2A 1200 kg car travelling at 15 m/s crashes and stops in 0.10 s. Calculate the average force on it.[3 marks]
    1. Δv = 15 m/s
    2. F = 1200 × 15 ÷ 0.10
    3. F = 180,000 N
    Q3A force of 2000 N acts on an 800 kg car for 0.50 s. Calculate its change in velocity.[3 marks]
    1. Rearrange: Δv = F × Δt ÷ m
    2. Δv = 2000 × 0.50 ÷ 800
    3. Δv = 1.25 m/s

    Endless practice

    A new question every time, marked instantly. Work it out on paper, then type your answer.

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    Frequently asked questions

    What is the equation linking force and momentum change?

    Force = change in momentum ÷ time taken, or F = mΔv/Δt. Force is in N, mass in kg, change in velocity in m/s and time in s.

    How do airbags reduce injuries?

    They increase the time over which your momentum changes to zero. For the same change in momentum, a longer time means a smaller force on you.

    Is this equation Higher tier?

    Yes. In AQA, force and changes in momentum are GCSE Physics (separate science) only, Higher tier.