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Answers
Answer:
In any equation, all terms on both sides must have the same units. Since we know that this equation gives us the value of 'S', the displacement, all three terms on the right side must also have the units of displacement, i.e, [L].
A is on its own, hence, it has the units of displacement, [L]
Bt must have dimensions [L], and t has dimensions [T]. So, B must have dimensions [L]([T]^-1)
Ct^2 must also have dimensions [L], and t^2 has dimensions [T^2]. So, C must have dimensions [L]([T]^-2)
Explanation:
whenever two physical quantities are added, they must have same dimensions. hence LHS & RHS dimensions must match. we know that unit of s is m, hence its dimension is L^1
dimension of a will also be same as s, i.e L^1. units of b will be m/s, therefore its dimensions will be L^1 T^-1. units of c will be m/s^2, dimensions of c will be
L^1 T^-2