Force and change in momentum: F = mΔv/Δt
Force = change in momentum ÷ time taken. AQA writes it as F = m Δv/Δt. F is the force in newtons (N), m is the mass in kilograms (kg), Δv is the change in velocity in m/s and Δt is the time in seconds (s). It is a Higher tier equation, and where a specification includes it, the exam sheet prints it.
Equation
F = Δp ÷ t
| Symbol | Quantity | Unit |
|---|---|---|
F | force | N |
Δp | change in momentum | kg·m/s |
t | time | s |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Given on the sheet · Higher tier only | F = m Δv/Δt |
| AQA Combined Science (8464) | Not in this specification | |
| Edexcel Physics (1PH0) | Given on the sheet · Higher tier only | F = (m v − m u)/t |
| Edexcel Combined Science (1SC0) | Given on the sheet · Higher tier only | F = (m v − m u)/t |
| OCR Gateway Physics A (J249) | Not in this specification | |
| OCR Twenty First Century Physics B (J259) | Not in this specification |
Calculator: F = Δp ÷ t
Equation
Δp = F t
| Symbol | Quantity | Unit |
|---|---|---|
Δp | change in momentum | kg·m/s |
F | resultant force | N |
t | time | s |
What each specification says
| Exam board | Status | Equation |
|---|---|---|
| AQA Physics (8463) | Not in this specification | |
| AQA Combined Science (8464) | Not in this specification | |
| Edexcel Physics (1PH0) | Not in this specification | |
| Edexcel Combined Science (1SC0) | Not in this specification | |
| OCR Gateway Physics A (J249) | Not in this specification | |
| OCR Twenty First Century Physics B (J259) | Given on the sheet · Higher tier only | Δp = F t |
Calculator: Δp = F t
What the equation tells you
Momentum is mass times velocity, as the momentum equation shows. This equation says how fast that momentum changes. A big change in a short time needs a big force.
Car safety uses the idea in reverse. A crash always removes the same momentum from you, because you go from moving to still. Crumple zones, seat belts and airbags make that change take longer. A longer time means a smaller force on your body.
It also explains why you bend your knees when you land from a jump, and why a cricket fielder pulls the hands back as the ball arrives.
Three boards, three printed forms
The physics is the same everywhere, but the boards print it in different ways. Use the one on your own paper.
- AQA Physics (8463): F = m Δv/Δt. It is Higher tier and belongs to the separate Physics course only, so Combined Science Trilogy (8464) leaves it out.
- Edexcel (1PH0 and 1SC0): F = (mv − mu)/t, where u is the starting velocity and v the final one. It is Higher tier in both Physics and Combined Science.
- OCR Twenty First Century (J259): change in momentum = resultant force × time, printed as Δp = F t. It is Higher tier.
- OCR Gateway (J249) does not list this relationship.
Every version that appears is on the given list, the equations you select from the sheet and apply. Read the full lists on the AQA page or the OCR Twenty First Century page.
Link to F = ma
Change in velocity divided by time is acceleration. So m Δv ÷ Δt is the same as m × a, which is Newton's second law. Questions with a short impact time, such as a kick or a crash, are easier to set up with the momentum form.
Worked examples
F
- Change the contact time to seconds: 15 ms = 0.015 s
- F = m Δv ÷ Δt
- F = 0.45 × 20 ÷ 0.015
- F = 9 ÷ 0.015
- F = 600 N
600 N
Δt
- Δt = m Δv ÷ F
- Δt = 1200 × 12 ÷ 24 000
- Δt = 14 400 ÷ 24 000
- Δt = 0.6 s
0.6 s
Δp
- This uses the OCR J259 form: Δp = F t
- Δp = 30 × 2.5
- Δp = 75 kg m/s
75 kg m/s
Common mistakes
- Putting in the final velocity instead of the change. A ball that goes from 5 m/s to 25 m/s has Δv = 20 m/s.
- Leaving a contact time in milliseconds. A 15 ms kick entered as 15 makes the force 1000 times too small.
- Ignoring direction when something bounces. A ball that hits a wall at 8 m/s and returns at 6 m/s changes velocity by 14 m/s.
- Thinking a crumple zone lowers the change in momentum. It keeps the change the same and stretches the time.
Rearrange this equation for Δt or m in the Equation Rearranger.
Questions people ask
Is this in Combined Science?
It depends on the board. Edexcel Combined Science (1SC0) includes it at Higher tier. AQA Trilogy (8464) does not.
What unit does momentum change have?
Kilogram metres per second, written kg m/s. A newton second (N s) is the same size, since 1 N is 1 kg m/s².