Question

If $x=a+bt+c{t}^2$, where $x$ is in meter and $t$ is in second. What is the unit of $b$ and $c$ ?

Answer 1

Dimension of $a,bt,c{t}^2$ should be equal to x

$x=\left[L\right]$

So, the dimension of bt will be equal to that of 'x'.

$bt=\left[L\right]$

$b=\frac{\left[L\right]}{\left[T\right]}$

$b=\left[L{T}^{-1}\right]$

The dimension of c can be obtained as:

$c{t}^2=\left[L\right]$

$c=\frac{\left[L\right]}{\left[T^2\right]}$

$c=\left[L{T}^{-2}\right]$