Physics

The distance traveled by a body in time $$'t'$$ is given by $$x=a+bt+{ ct }^{ 2 }$$ where $$x$$ is distance, $$t$$ is time $$a, b$$ and $$c$$ are constants. The dimensional formula for $$a, b$$ and $$c$$ respectively are :


ANSWER

$$L^1, { L }^{ 1 }{ T }^{ -1 },{ L }^{ 1 }{ T }^{ -2 }$$


SOLUTION

$$ x ={a+bt+ct^{2}}$$

$$L^1=a$$
$$L^1=bt $$
$$\Rightarrow b=L^1T^{-1}$$
$$cT^{2}= L\Rightarrow c=L^1T^{-2}$$
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