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RMS speed
v_rms = √(3RT/M)
Where: M = mass (kg), R = range / radius / resistance, T = time period (s) / temperature (K) / tension (N), vᵣₘₛ = RMS speed
Solved example
Given: M = 7, R = 5, T = 10
Find: v_rms (RMS speed)
- Formula: vᵣₘₛ = √(3)·√(R·T/M)
- Substitute the values: vᵣₘₛ = √(3)·√(10·5/7)
- Result: vᵣₘₛ = 4.6291 m/s
Answer: v_rms = 4.6291 m/s
Calculator
How to calculate RMS speed
- Write down the formula: v_rms = √(3RT/M).
- Note the known values (M, R, T).
- Substitute them and simplify to find v_rms.
- Use the calculator above to solve for any letter.
Frequently asked questions
What is the formula for RMS speed?
The formula is v_rms = √(3RT/M), where M = mass (kg), R = range / radius / resistance, T = time period (s) / temperature (K) / tension (N), vᵣₘₛ = RMS speed.
What is RMS speed when M = 7, R = 5, T = 10?
v_rms = 4.6291 m/s. Substitute the values into v_rms = √(3RT/M) and simplify.
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