Question

Express the following derived units in terms of the fundamental units of length, mass and time.

1) Speed

2) Area

3) Acceleration

4) Density

5) Volume

Answer 1

(i) $Speed=\frac{Distance}{Time}=\frac{Length}{Time}$

(ii) $Area=Length\times Breadth=Length\times Length={\left(Length\right)}^2$

(iii) $Acceleration=\frac{Velocity}{Time}$

$=\frac{Displacement}{Time\times Time}=\frac{Length}{{\left(Time\right)}^2}$

(iv) $Density=\frac{Mass}{Volume}$

$=\frac{Mass}{Length\times Length\times Length}=\frac{Mass}{{Length}^3}$

(v) $Volume=Length\times Breadth\times Height$
$=Length\times Length\times Length$
$={\left(Length\right)}^3$