Find the kinetic energy of a 4 kg particle whose velocity is $$ (\hat{i}-\hat{j}) \mathrm{ms} $$

Question

UpStudy AI · Accepted Answer

To calculate the **kinetic energy** of a particle, you can use the formula:

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

where:
- $$ K $$ is the kinetic energy,
- $$ m $$ is the mass of the particle,
- $$ v $$ is the speed of the particle.

Given:
- Mass ($$ m $$) = **4 kg**
- Velocity vector ($$ \vec{v} $$) = $$ \hat{i} - \hat{j} \, \text{m/s} $$

**Step 1: Determine the Speed ($$ v $$)**

The speed is the magnitude of the velocity vector.

$$
v = |\vec{v}| = \sqrt{(1)^2 + (-1)^2} = \sqrt{1 + 1} = \sqrt{2} \, \text{m/s}
$$

**Step 2: Calculate the Kinetic Energy ($$ K $$)**

$$
K = \frac{1}{2} \times 4 \, \text{kg} \times (\sqrt{2} \, \text{m/s})^2
$$

$$
K = \frac{1}{2} \times 4 \times 2
$$

$$
K = \frac{1}{2} \times 8 = 4 \, \text{Joules}
$$

**Final Answer:**

The kinetic energy of the particle is **4 Joules**.
The kinetic energy of the particle is 4 Joules.

Find the kinetic energy of a 4 kg particle whose velocity is