In the expression $x = a t + b t^2$, $x$ is the distance travelled by a body in kilometers and $t$ i

Question

In the expression $x = a t + b t^2$, $x$ is the distance travelled by a body in kilometers and $t$ is the time in seconds. What are the units of $b$?

Professor PC Thomas Classes · Answer

By the principle of homogeneity, each term must have the same units as $x$. Thus, the unit of $b t^2$ must be km. Therefore, $	ext{unit of } b 	imes (	ext{s})^2 = 	ext{km} \implies 	ext{unit of } b = 	ext{km s}^{-2}$.