Final answer:
The formula for V in terms of k and m, derived from k = (1/2)mv², is V = √((2k)/m) by multiplying by 2, dividing by m, and taking the square root.
Step-by-step explanation:
To find the formula for V in terms of k and m from the given equation k = (1/2)mv², we can follow these steps:
- Multiply both sides of the equation by 2 to eliminate the fraction: 2k = mv².
- Divide both sides of the equation by m to isolate v² on one side: (2k)/m = v².
- Take the square root of both sides to solve for v: v = √((2k)/m).
Thus, the formula for V in terms of k and m is V = √((2k)/m).