Answer to Question #101808 in Calculus for Kampamba

Question

If velocity ,time and force were chosen as basic quanties ,find the dimensions of mass

Answer 1

Solution. From Newton’s second law

$$F=ma$$

where F is force; m is mass; a is acceleration.

By definition of acceleration

$$a=\frac {\Delta v}{\Delta t}$$

where Δv is speed change; Δt is time. Substituting the second formula in the first we get

$$F=m\frac {\Delta v}{\Delta t} \implies m= \frac {F \Delta t} {\Delta v}=F \Delta t(\Delta v)^{-1}$$

Thus, the dimension of mass is

$$[m]=N \cdot s^2 \cdot m^{-1}$$