Dimensions of a and b in the relation p=b-x^2/at

The given relation is p = b - x^2 / at, where p is power, x is distance, and t is time. To derive the dimensions of a and b, we need to use the concept of dimensional analysis.

Dimensional Analysis
Dimensional analysis is a technique used to derive the relationship between physical quantities. It involves analyzing the dimensions of the quantities involved in a given equation.

Step 1: Analyzing the Dimensions of the Given Quantities
We know that power is measured in watts (W), distance is measured in meters (m), and time is measured in seconds (s). Therefore, we can represent the dimensions of power, distance, and time as follows:

- [p] = ML^2T^-3 (where M represents mass, L represents length, and T represents time)
- [x] = L
- [t] = T

Step 2: Deriving the Dimensions of a and b
We can now analyze the dimensions of the given relation p = b - x^2 / at. Since the right-hand side of the equation is a subtraction of two terms, we need to ensure that the dimensions of both terms are the same.

- Dimension of the first term (b): [b] = ML^2T^-3
- Dimension of the second term (x^2 / at): [x^2 / at] = L^2 / (T x T) = L^2T^-2

Since the dimensions of the first term and the second term are not the same, we can conclude that the dimensions of a and b cannot be derived from the given relation.

Conclusion
We cannot derive the dimensions of a and b from the given relation p = b - x^2 / at. Therefore, the question is incomplete or incorrect.

A=M^-1T^2
B=L^2