Question

What is the root mean square value of the following velocity components: 2.0 m/s, -3.0 m/s, and 4.0 m/s?

A) 3.3 m/s
B) 1.0 m/s
C) 3.1 m/s
D) 1.9 m/s
E) 5.4 m/s

Answer 1

The root mean square value of the velocity components 2.0 m/s, -3.0 m/s, and 4.0 m/s is 3.1 m/s, corresponding to option C.

Step-by-step explanation:

The question is asking for the root mean square value of the velocity components given as 2.0 m/s, -3.0 m/s, and 4.0 m/s. The root mean square (RMS) value is a statistical measure of the magnitude of a varying quantity. It is calculated by squaring each component, finding the average of these squares, and then taking the square root of this average.

To find the RMS value:

• Square each component: (2.0)^2 = 4, (-3.0)^2 = 9, (4.0)^2 = 16
• Find the average of these squares: (4 + 9 + 16) / 3 = 29 / 3
• Take the square root of the average: √(29 / 3) = √9.67 ≈ 3.1 m/s

Therefore, the RMS value of the velocity components is 3.1 m/s, which corresponds to option C.