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

Question

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−−−−√

Answer 1

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:

$$V_t=\sqrt{\frac{w}{2dA{C}_d}}$$

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:

$$V_t=\sqrt{\frac{w}{2dA{C}_d}}$$