The kinetic energy of an object of mass m moving with velocity 5 m/s is 25 J. If velocity of this object increased by three times, then kinetic energy will be :

Question

Accepted Answer

To determine the kinetic energy of the object when its velocity is increased by three times, we start by understanding the formula for kinetic energy:

$$ KE = \frac{1}{2} m v^2 $$

Initially, the object has a velocity of 5 m/s and a kinetic energy of 25 J. Using the kinetic energy formula, we can express this as:

$$ 25 = \frac{1}{2} m (5)^2 $$

$$ 25 = \frac{1}{2} m \times 25 $$

From this equation, we can solve for the mass $ m $:

$$ m = 2 \, \text{kg} $$

Now, if the velocity is increased by three times, the new velocity $ v' $ is:

$$ v' = 3 \times 5 = 15 \, \text{m/s} $$

We can now calculate the new kinetic energy $ KE' $ using the new velocity:

$$ KE' = \frac{1}{2} m (v')^2 $$

Substituting the known values:

$$ KE' = \frac{1}{2} \times 2 \times (15)^2 $$

$$ KE' = 1 \times 225 $$

$$ KE' = 225 \, \text{J} $$

Therefore, the kinetic energy of the object when its velocity is increased by three times is 225 J, which corresponds to Option 1.

**Explanation for Incorrect Options:**

- **Option 2 (75 J):** This option is incorrect because it does not account for the fact that kinetic energy is proportional to the square of the velocity. Simply tripling the velocity results in a ninefold increase in kinetic energy, not a threefold increase.

- **Option 3 (450 J):** This option is incorrect because it overestimates the kinetic energy. The calculation shows that the kinetic energy is 225 J, not 450 J.

- **Option 4 (375 J):** This option is incorrect because it also overestimates the kinetic energy. The correct calculation results in 225 J, not 375 J.

Thus, the correct answer is indeed Option 1, as it accurately reflects the increase in kinetic energy when the velocity is tripled.