The distance covered by s=a+ bt+ ct find the dimension.
To determine the dimensions of the expression s = a + bt + ct, we need to break down each term and analyze their dimensions individually.
Let's start with the variable s, which represents distance. Distance is usually measured in units such as meters (m), feet (ft), or kilometers (km). Therefore, the dimension of s is [L], representing length.
Next, we have the term a. Since a is added to s in the expression, it must have the same dimension as s, which is [L].
Moving on to the term bt, the variable b represents a coefficient multiplying the variable t. From the equation, it is clear that t represents time. Time is typically measured in seconds (s), minutes (min), or hours (h). Therefore, the dimension of t is [T], representing time. When b is multiplied by t, the resulting dimension becomes [L][T]^-1, as the time unit in the denominator cancels out with the dimension of [T] in t.
Lastly, we consider the term ct. Similar to bt, c represents a coefficient multiplying t. Therefore, the dimension of this term is also [L][T]^-1.
Adding up all the terms, we have:
s = (a) + (b * t) + (c * t)
= [L] + [L][T]^-1 + [L][T]^-1
Simplifying the expression, we can rewrite it as follows:
s = [L] + ([L][T]^-1) + ([L][T]^-1)
= [L] + [L][T]^-1 + [L][T]^-1
= [L] + 2[L][T]^-1
Therefore, the overall dimension of the expression s = a + bt + ct is:
[L] + [L][T]^-1 + [L][T]^-1
This can also be written as [L] + 2[L][T]^-1, representing a length dimension plus two length divided by time dimensions.