Question

If $x=at+b{t}^2$, where x is in metres and t is in seconds, which one of the following should be the unit of a?

• A. $m{s}^{-2}$
• B. $m{s}^{-1}$
• C. m
• D. $m^2{s}^{-1}$

Answer 1

The correct option is B $m{s}^{-1}$

The relation between the position and time is given as:

$x=at+b{t}^2$

$x$ is in meters and $t$ is in seconds.

Using the principle of homogeneity, the dimension of $X$ will be similar to that of $at$.

$x=m,t=s$

$\left[m\right]=a\left[s\right]$

$a=m{s}^{-1}$

option $\left(B\right)$ is correct.