Which is the equation for terminal velocity?(1 point)

Question

Responses

Vt=w2dACd−−−−−√
upper V subscript t baseline equals Start Root Start Fraction w over 2 d upper A Upper C subscript d baseline End Fraction End Root

Vt=2wdACd−−−−√
upper V subscript t baseline equals Start Root Start Fraction 2 w over d upper A Upper C subscript d baseline End Fraction End Root

Vt=2mdACd−−−−√
upper V subscript t baseline equals Start Root Start Fraction 2 m over d upper A Upper C subscript d baseline End Fraction End Root

Vt=dACd2w−−−−√

Answer 1

The equation for terminal velocity (\(V_t\)) can be expressed as:

\[ V_t = \sqrt{\frac{2mg}{\rho A C_d}} \]

where:

• \(m\) is the mass of the object,
• \(g\) is the acceleration due to gravity,
• \(\rho\) is the density of the fluid through which the object is falling,
• \(A\) is the cross-sectional area of the object,
• \(C_d\) is the drag coefficient.

From the options provided in the question, none of them appear precisely correct in standard form. However, the closest option is:

\[ V_t = \sqrt{\frac{2w}{d A C_d}} \]

where \(w\) could represent weight, relating to \(mg\) (weight = mass × gravity), \(d\) may relate to density in some contexts, but it is not the most standard representation. Thus, please consider that the direct formula for terminal velocity may not be represented accurately in your options. If you were choosing one that could relate, it might be the first option, understanding the context of symbols used.