Can we check the correctness of a physical equation by the dimension ? IF so , name the principle.

Check the correctness of the following equation by the method of dimensions. s=ut+1/2at^2

Name the principle used to check the correctness of an equation.

Name three physical quantities having same dimension.

A stone is thrown upwards from the ground with a velocity, u . a)What is the maximum height attained by the stone? b)Check the correctness of the equation obtained in,(a)using the method of dimensional analysis. c)Draw the position-time graph of the stone during its return journey

The correctness of equations can be checked using the principle of homogeneity. State the principle of homogeneity.