Three particles are travelling in the same plane with velocities as shown in the vector diagram - AQA - A-Level Physics - Question 10 - 2021 - Paper 2
Question 10
Three particles are travelling in the same plane with velocities as shown in the vector diagram.
What is the root mean square speed of the particles?
Worked Solution & Example Answer:Three particles are travelling in the same plane with velocities as shown in the vector diagram - AQA - A-Level Physics - Question 10 - 2021 - Paper 2
Step 1
Calculate the Squared Velocities
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Answer
First, we need to find the square of the velocities for each particle:
For the first particle, the velocity is 2m s−1, so its squared velocity is (2)2=4m2s−2.
For the second particle, the velocity is 4m s−1, so its squared velocity is (4)2=16m2s−2.
For the third particle, the velocity is 6m s−1, so its squared velocity is (6)2=36m2s−2.
Step 2
Sum the Squared Velocities
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Answer
Now sum the squared velocities:
4+16+36=56m2s−2
Step 3
Calculate the Root Mean Square Speed
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Answer
To find the root mean square speed, calculate the mean of the squared velocities and then take the square root:
Calculate the mean:
Mean=356=356≈18.67m2s−2
Take the square root:
RMS Speed=18.67≈4.32m s−1
Thus, rounding gives approximately 4.3m s−1, which matches answer choice A.
