Question

If $x=at+b{t}^2$, where $x$ is the distance travelled by the body in $\text{km}$ and $t$ is the time taken by it in $\text{s}$, then the unit of $b$ will be

• A. $\text{km/s}$
• B. $\text{km-s}$
• C. ${\text{km/s}}^2$
• D. ${\text{km-s}}^2$

Answer 1

The correct option is C ${\text{km/s}}^2$

Given,
$x=at+b{t}^2$
We know that physical quantities having the same dimensions are added or subtracted.
Therefore, the dimension of $at$ should be the same as the dimension of $b{t}^2$.
Also, physical quantities having the same dimensions can be compared.
Therefore, the dimension of $at+b{t}^2$ should be the same as the dimension of $x$.
$\Rightarrow \left[b{t}^2\right]=\left[x\right]$
$\Rightarrow \left[b\right]=\left[x{t}^{-2}\right]$
$\Rightarrow \left[b\right]=\left[L{T}^{-2}\right]$
Hence, the unit of $b$ will be ${\text{km/s}}^2$