Work Done Calculation

This problem requires calculating the work done to change the kinetic energy of a car.

Work-Energy Theorem Principle

The work done on an object equals the change in its kinetic energy. The formula is: $W = \Delta KE = KE_{final} - KE_{initial}$ where kinetic energy ($KE$) is given by $KE = \frac{1}{2}mv^2$. $m$ is mass and $v$ is velocity.

Given Data

• Mass ($m$): 120 kg
• Initial Speed ($v_i$): 72 km/h
• Final Speed ($v_f$): 108 km/h

Step-by-Step Calculation

1. Convert Speeds to m/s: Speeds must be in meters per second (m/s) for energy calculations. Use the conversion factor $1 \text{ km/h} = \frac{5}{18} \text{ m/s}$.
   • $v_i = 72 \text{ km/h} \times \frac{5}{18} \text{ m/s} = 20 \text{ m/s}$
   • $v_f = 108 \text{ km/h} \times \frac{5}{18} \text{ m/s} = 30 \text{ m/s}$
2. Calculate Initial Kinetic Energy ($KE_i$): $KE_i = \frac{1}{2}mv_i^2 = \frac{1}{2} \times 120 \text{ kg} \times (20 \text{ m/s})^2$ $KE_i = 60 \times 400 = 24000 \text{ J}$
3. Calculate Final Kinetic Energy ($KE_f$): $KE_f = \frac{1}{2}mv_f^2 = \frac{1}{2} \times 120 \text{ kg} \times (30 \text{ m/s})^2$ $KE_f = 60 \times 900 = 54000 \text{ J}$
4. Calculate Work Done ($W$): $W = KE_f - KE_i = 54000 \text{ J} - 24000 \text{ J}$ $W = 30000 \text{ J}$
5. Express in Scientific Notation: $W = 3.0 \times 10^4 \text{ J}$

Final Answer

The work done to raise the car's speed is $3.0 \times 10^4 \text{ J}$.