The distance d that a certain particle moves may be calculated from the expression d = at + bt2 where a and b are constants; and t is the elapsed time. what must the dimensions of the quantities a and b be, respectively?

Guven that the distance d that a certain particle moves may be calculated from the expression where a and b are constants; and t is the elapsed time.

Distance is a length and hence the dimension of distance is L.

Now, and also will have the dimension of L.

Time has a dimension of T.

For , let the dimension of be , then


For , let the dimension of be , then


Therefore, the dimension of is while the dimension of is .