Question

If $x=at+b{t}^2$, where $x$ is the distance travelled by the body in kilometers while $t$ is the time in seconds, then the unit of $b$ is

• A. $\text{Km/s}$
• B. ${\text{Km/s}}^2$
• C. $\text{Kms}$
• D. ${\text{Kms}}^2$

Answer 1

The correct option is B ${\text{Km/s}}^2$

Given the equation $x=at+b{t}^2$, so, using Principle of Homogeneity we have
$\left[x\right]=\left[at\right]=\left[b{t}^2\right]$
$\Rightarrow \left[L\right]=b\left[T^2\right]\Rightarrow b=\left[L{T}^{-2}\right]$
Hence, the unit will be ${\text{km/s}}^2$