Final answer:
To verify the correctness of the formula s=ut+(1/2)at^2, dimensional analysis is performed. Both terms, ut and (1/2)at^2, have the same dimension [L], confirming the equation is dimensionally consistent, suggesting it is potentially correct.
Step-by-step explanation:
To check the correctness of the formula s=ut+\frac{1}{2}at^2, we will use dimensional analysis to verify whether the equation is dimensionally consistent. The dimensions for displacement (s), initial velocity (u), acceleration (a), and time (t) are [L], [LT−¹], [LT−²], and [T], respectively. We add the dimensions of ut and \frac{1}{2}at^2 to see if they equate to [L], the dimension for displacement.
The term ut has dimensions [LT−¹] × [T] = [L], and the term \frac{1}{2}at^2 has dimensions [LT−²] × [T]2 = [L]. Since both terms equate to [L] when dimensions are considered, and we are simply adding these two terms together, we can confirm the equation is dimensionally consistent and potentially correct.