Question
Which is the equation for terminal velocity?(1 point)
Responses
Vt=dACd2w−−−−√
upper V subscript t baseline equals Start Root Start Fraction d upper A Upper C subscript d baseline over 2 w 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=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=w2dACd−−−−−√
Responses
Vt=dACd2w−−−−√
upper V subscript t baseline equals Start Root Start Fraction d upper A Upper C subscript d baseline over 2 w 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=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=w2dACd−−−−−√
Answers
Answered by
GPT-4o mini
The equation for terminal velocity is typically expressed as:
\[
V_t = \sqrt{\frac{2mg}{\rho C_d A}}
\]
where:
- \( V_t \) is the terminal velocity,
- \( m \) 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 moving,
- \( C_d \) is the drag coefficient,
- \( A \) is the cross-sectional area of the object.
From the provided responses, the closest form that resembles the standard equation for terminal velocity is not explicitly written correctly, as they all seem to be misformatted. However, if we focus on the logical structure, none of the provided options accurately represent the standard equation for terminal velocity correctly.
If you need to select one based on terminology or closest resemblance to physical principles, you could analyze the formulas one by one, but it is important to recognize that all of them appear to have different variables or terms. The concept of terminal velocity is fundamentally based on balancing forces, mainly weight and drag.
\[
V_t = \sqrt{\frac{2mg}{\rho C_d A}}
\]
where:
- \( V_t \) is the terminal velocity,
- \( m \) 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 moving,
- \( C_d \) is the drag coefficient,
- \( A \) is the cross-sectional area of the object.
From the provided responses, the closest form that resembles the standard equation for terminal velocity is not explicitly written correctly, as they all seem to be misformatted. However, if we focus on the logical structure, none of the provided options accurately represent the standard equation for terminal velocity correctly.
If you need to select one based on terminology or closest resemblance to physical principles, you could analyze the formulas one by one, but it is important to recognize that all of them appear to have different variables or terms. The concept of terminal velocity is fundamentally based on balancing forces, mainly weight and drag.