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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