Dimensional Analysis Practice Problems

A car is moving with speed v, given by the equation: $v=C+Dt^2$ , where $t$ represents time and C and D are constants. Determine the SI units of C and D.

Assume that the equation to calculate a woman's blood volume V (in Liters) is V = 0.3561 H³ + 0.03308W + 0.1833, where H (in meters) and W (in kilograms) represent the height and weight of the woman. Determine the units of the numbers 0.3561, 0.03308, and 0.1833

The motion of an object moving along a straight path is represented by a time-dependent position equation: x = 3 + 5t, where x is in meters and t is in seconds. What do the numbers 3 and 5 represent?

The following relation represents a physical quantity called drag force, F = Cρ^αv^βA^γ where α, β, γ, and C are dimensionless quantities. ρ is the density of fluid, v is the velocity and A is the cross-sectional area. Using dimensional analysis, determine the formula of drag force.

Find the dimensions of the quantity P formed by the following combination: P = √[1/(ϵ₀​μ₀)]. The fundamental constants are ϵ₀ (vacuum permittivity), and μ₀​ (vacuum permeability).

What should be the dimensions of the quantity R formed by the following combination: R = √[(hc)/G] where G (gravitational constant), h (Planck's constant), and c (speed of light) are three universal constants.