For the basic dimensions we'll assign:
M = mass, L = length, T = time
Speed is given by change in distance over time:
speed = L/T = LT⁻¹
Density is given by mass divided by volume, where volume is a quantity that only exists in 3 spatial dimensions:
density = M/L³ = ML⁻³
Length is quite simple:
Length = L
Impulse is given by the product of mass and velocity, where velocity is change in displacement over time:
impulse = M(L/T) = MLT⁻¹
Angle is given by arc length divided by radius:
angle = L/L = L⁰
Angles have no unit, but we still add a label to distinguish between different systems of measurement (turn, degree, radian, gradian).
We can see that length is the only quantity which isn't derived from other quantities. The correct answer is Choice C.
