An object has a mass of 10 kg and is moving at a speed of 8 m/s. What is its kinetic energy?
An object has a mass of 5 kg and is moving at a speed of 12 m/s. What is its kinetic energy?
The kinetic energy (KE) of an object can be calculated using the formula:

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

where \( m \) is the mass of the object and \( v \) is its speed.

1. For the first object with a mass of 10 kg and a speed of 8 m/s:

\[
KE = \frac{1}{2} \times 10 \, \text{kg} \times (8 \, \text{m/s})^2
\]
\[
KE = \frac{1}{2} \times 10 \times 64
\]
\[
KE = 5 \times 64 = 320 \, \text{J}
\]

So, the kinetic energy of the first object is **320 Joules**.

2. For the second object with a mass of 5 kg and a speed of 12 m/s:

\[
KE = \frac{1}{2} \times 5 \, \text{kg} \times (12 \, \text{m/s})^2
\]
\[
KE = \frac{1}{2} \times 5 \times 144
\]
\[
KE = 2.5 \times 144 = 360 \, \text{J}
\]

So, the kinetic energy of the second object is **360 Joules**.
A classic physics problem!

The kinetic energy of an object is given by the formula:

Kinetic Energy (KE) = 0.5 × mass (m) × velocity (v)²

Let's apply this formula to each object:

**Object 1:**
Mass (m) = 10 kg
Velocity (v) = 8 m/s

KE = 0.5 × 10 kg × (8 m/s)²
= 0.5 × 10 kg × 64 m²/s²
= 320 J

**Object 2:**
Mass (m) = 5 kg
Velocity (v) = 12 m/s

KE = 0.5 × 5 kg × (12 m/s)²
= 0.5 × 5 kg × 144 m²/s²
= 360 J

So, the kinetic energy of Object 1 is 320 J, and the kinetic energy of Object 2 is 360 J.