If x=a+bt+ct^{2 where x is in metres and t is in seconds.What is the unit of c?}

The dimension of ct^{2} should be [L] since the left side of the equation has dimension [L].

Thus,

[L] = [c][T^{2}]

=> [c] = [LT^{-2}]

So, the unit of c is ms^{-2}.

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