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

Responses

Vt=w/2dACd−−−−−√
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=2m/dACd−−−−√
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=dAC/d2w−−−−√
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=2w/dACd−−−−√

1 answer

The correct equation for terminal velocity (\( V_t \)) of an object falling under the influence of gravity in a viscous medium is generally given by:

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

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 provided options, the equation that resembles the correct form for terminal velocity is:

\[ V_t = \sqrt{\frac{w}{2dAC_d}} \]

where \( w \) can be interpreted as the weight (which is \( mg \)), \( d \) as the density of the fluid, \( A \) as the cross-sectional area, and \( C_d \) as the drag coefficient.

Thus, the correct response is:

\[ V_t = \sqrt{\frac{w}{2dAC_d}} \]