To determine the kinetic energy of a cyclist with a mass of 70 kg biking at a speed of 7 m/s, we will use the formula for kinetic energy:
[tex]\[ E_k = \frac{1}{2} mv^2 \][/tex]
Here, [tex]\( m \)[/tex] represents the mass of the cyclist, and [tex]\( v \)[/tex] represents the velocity. Let's break this down step-by-step:
1. Identify the given values:
- Mass ([tex]\( m \)[/tex]) = 70 kg
- Velocity ([tex]\( v \)[/tex]) = 7 m/s
2. Insert these values into the kinetic energy formula:
[tex]\[ E_k = \frac{1}{2} \times 70 \,\text{kg} \times (7 \,\text{m/s})^2 \][/tex]
3. Calculate the square of the velocity:
[tex]\[ v^2 = (7 \,\text{m/s})^2 = 49 \,\text{m}^2/\text{s}^2 \][/tex]
4. Multiply the mass by the squared velocity:
[tex]\[ m \times v^2 = 70 \,\text{kg} \times 49 \,\text{m}^2/\text{s}^2 = 3430 \,\text{kg} \cdot \text{m}^2/\text{s}^2 \][/tex]
5. Finally, divide by 2 to find the kinetic energy:
[tex]\[ E_k = \frac{3430 \,\text{kg} \cdot \text{m}^2/\text{s}^2}{2} = 1715 \,\text{J} \][/tex]
Therefore, the kinetic energy of the cyclist is [tex]\( 1715 \)[/tex] Joules.
