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The given problem states that the kinetic energy \( K \) of an object is given by the formula:

\[
K = \frac{1}{2}mv^2
\]

where:
- \( m \) is the mass of the object in kilograms (kg),
- \( v \) is the velocity of the object in meters per second (m/s).

We are also provided with an alternative expression for the kinetic energy as:

\[
K = 34v^2
\]

We need to find the mass \( m \) of the object.

### Step-by-Step Solution:
We know the general equation for kinetic energy is:

\[
K = \frac{1}{2} m v^2
\]

This can be set equal to the alternative expression for kinetic energy:

\[
\frac{1}{2} m v^2 = 34 v^2
\]

We can cancel out \( v^2 \) on both sides, assuming \( v \neq 0 \):

\[
\frac{1}{2} m = 34
\]

Now, solve for \( m \):

\[
m = 34 \times 2 = 68 \, \text{kg}
\]

Thus, the mass of the object is **68 kilograms**.

Would you like more details or have any further questions?

### 5 Related Questions:
1. What would the mass be if the equation for kinetic energy was \( K = 50v^2 \)?
2. How does kinetic energy depend on velocity if the mass is constant?
3. If the velocity doubles, what happens to the kinetic energy?
4. Can you derive the formula for kinetic energy from basic principles?
5. How would the kinetic energy change if the mass of the object were halved?

### Tip:
Always remember that kinetic energy is proportional to the square of velocity, meaning even small changes in velocity cause significant changes in energy.

The kinetic energy K of an object is given by the formula K = 1/2mv^2, where m is the mass of the object, and v is its velocity. If the kinetic energy of a certain object is K = 34v^2, what is the mass of the object?

Learn how to find the mass of an object using the kinetic energy formula K = 1/2 mv^2 and a provided equation K = 34v^2. This step-by-step solution involves basic algebra and is suitable for students in Grades 8-10.

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