Physics

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

##### SOLUTION
Dimension of $a,bt,c{ t }^{ 2 }$ should be equal to x
$x=[L]$

So, the dimension of bt will be equal to that of 'x'.
$bt=[L]$
$b=\dfrac{[L]}{[T]}$

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

The dimension of c can be obtained as:
$ct^2=[L]$
$c=\dfrac{[L]}{[T^2]}$

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

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