A has travels `x_(1)` when accelerates from rest at constant rate `a_(2)` for some time and after that travels a distance `x_(2)` when declelertes at a constant rate `a_(2)` to come to rest A student established a reletion `x_(1) + x_(2) = (a_(1)a_(2) t^(2))/(2(a_(1) +a_(2)))` choose the correct option (s)

Options

A. The relation is dimensionally correct
B. The relation is dimensionally incorrect
C. The relation may be dimensionally correct
D. None of the above

Answer

a

Explanation

LHS `= [x_(1) + x_(2)] = [x_(1)] = [x_(2)] = [M^(0)LT^(0)]`
RHS `= [(a_(1)a_(2)t^(2))/(2(a_(1) + a_(2)))]`
`= ([LT^(-2)] [LT^(-2)] [T^(-2)])/([LT^(-2)]) = [M^(0)LT^(0)]`
`:' LHS = RHS`
According to homogenetily principal, equation is dimensionally correct
Hence, option (a) is correct