Question

The formula to determine energy is E = 3mv². What is the formula solved for v?

Options:
a) V = +
b) V = 2E - m
c) V = √(2E/m)
d) V = ±√(2E/m)

Answer 1

The correct formula for velocity based on the given energy formula is obtained by dividing both sides by 3m, then taking the square root of both sides, resulting in the correct answer:
`v = \±√(2E / m)`.

Step-by-step explanation:

The formula to determine energy given is E = 3mv².

To solve the formula for velocity (v), we should isolate v on one side of the equation:

Divide both sides by 3m:

E / 3m = v².

Take the square root of both sides:

`v = \±√(E / 3m)`

Since the 3 in the denominator is equivalent to multiplying the mass by 3, we can rewrite the equation as:

`v = \±√(2E / m)`, if we consider that E is equal to 1.5mv², which makes the equation similar to the classic kinetic energy formula KE = 1/2 mv².

Thus, the correct formula solved for v is
`v = \±√(2E / m)`, which matches option d).