The distance covered by s=a + bt + ct find the dimension.

To determine the dimensions of a physical quantity, we need to break it down into its constituent parts and determine the dimensions of each part. In this case, we can break down the equation for distance covered, s, as follows:

s = a + bt + ct

Let's examine each term individually:

a: This term represents a constant. Since it has no coefficient or variable attached to it, we can assume it is dimensionless.

bt: Here, b is a constant and t represents time. The product of b and t will have the dimensions of distance. Thus, [bt] = [distance].

ct: Similarly, c is a constant and t represents time. The product of c and t will also have the dimensions of distance. Therefore, [ct] = [distance].

Now, adding up the terms, the dimensions of s, which represents the total distance covered, can be determined as:

[s] = [a + bt + ct]
= [dimensionless] + [distance] + [distance]
= [distance]

Therefore, the dimensions of distance covered, s, are expressed as [distance].