Question

The distance S an object travels under the influence of gravity in time t seconds is S(t)=1/2gt2+at+bgiven by where, (g is the acceleration due to gravity), a, b are constants.

Answer 1

The distance S an object travels under the influence of gravity in time t seconds is S(t)=b + at + 1/2 gt²

dimension of b = dimension of S

we know, dimension of S = [L]

so, dimension of b = [L]

dimension of {at} = dimension of S

or, dimension of a × dimension of t = dimension of S

or, dimension of a × [T] = [L]

or, dimension of a = [LT^-1]

hence, dimension of b = [L] and dimension of a = [LT^-1]