Question

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

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=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=dACd2w−−−−√

Answer 1

The equation for terminal velocity \( V_t \) for an object falling through a fluid is typically derived from balancing the forces acting on the object. The most commonly used equation is:

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

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

From the given options, the form that most closely matches this equation is:

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

However, the specific forms in your options do not correctly represent this equation. But if \( w = mg \) (the weight of the object), the correct choice that resembles it mathematically would be:

\[
V_t = \sqrt{\frac{w}{\frac{1}{2} \rho C_d A}}
\]

Please verify the specific context or modify the options if necessary.