The time dependence of a physical quantity P is give by P=P ₀ (- t^2 ) where is a constant and t is time. The constant will

Step-by-step solution

The given equation is P = P₀ (- t^2) . In any exponential function of the form e^x , the exponent x must be dimensionless. Therefore, the term t^2 must be dimensionless. [ t^2] = [M^0 L^0 T^0] = 1 . Since t represents time, its dimension is [T] . Thus, [ ] [T^2] = 1 . [ ] = [T⁻²] . This implies that the constant has dimensions of t⁻² . Answer: Have dimensions of t⁻²