A car of mass 1200 kg accelerates from rest to a speed of 20 m/s on a straight road. If the kinetic energy gained by the car is completely due to the work done by the engine, which of the following best represents the total kinetic energy acquired by the car at this speed?
240,000 joules
To find the total kinetic energy acquired by the car at a speed of 20 m/s, we start by using the formula for kinetic energy:
\(KE = \frac{1}{2}mv^2\)
- Step 1: Understand the components of the formula:
- \(m\) is the mass of the object, which is 1200 kg in this case.
- \(v\) is the velocity of the object, which is given as 20 m/s.
- Step 2: Substitute the known values into the formula
\(KE = \frac{1}{2} \times 1200 \, \text{kg} \times (20 \, \text{m/s})^2\)
- Step 3: Calculate the square of the velocity
\((20 \, \text{m/s})^2 = 400 \, \text{m}^2/\text{s}^2\)
- Step 4: Complete the kinetic energy calculation
\(KE = \frac{1}{2} \times 1200 \, \text{kg} \times 400 \, \text{m}^2/\text{s}^2\)
\(KE = 600 \times 400 = 240,000 \, \text{joules}\)
Thus, the total kinetic energy acquired by the car is 240,000 joules.
This confirms that the correct answer is 240,000 joules.
This solution demonstrates how to calculate kinetic energy using the mass and velocity of the object. Understanding this concept is essential for solving similar problems in physics and engineering.
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