The displacement y(t) of a particle depends on time according in equation y(t)=a_(1)t-a_(2)t^(2). What is the dimensions of a_(1) and a_(2)?

The displacement y(t) of a particle depends on time according in equat

1.	The displacement y(t) of a particle depends on time according in equation y(t)=a_(1)t-a_(2)t^(2). What is the dimensions of a_(1) and a_(2)?
Answer» SOLUTION :By the principle of homogeneity of dimensions, if the equation is CORRECT then `a_(1)t` and `a_(2)t^(2)` should have the same dimensions as that displacement `y(t)` i.e.[L]. i.e.`a_(1)t=[L],a_(1)=L/T=[LT^(-1)],a_(2)t^(2)=[L]=a_(2)=L/(T^(2))=[LT^(-2)]` So `[L]=[LT^(-1)]xx[T]-[LT^(-2)]XXT^(2)` or `[L]=[L]=[L]`. The EQUATIO is correct when the dimensions of `a_(1)` is `[LT^(-1)]` and that of `a_(2)` is `[LT^(-2)]`