Final answer:
The mass of the car with kinetic energy of 3.0 × 10^5 J traveling at 15 m/s is approximately 3000 kg when calculated using the kinetic energy formula. so, option a is the correct answer.
Step-by-step explanation:
The student has asked about determining the mass of the car given its kinetic energy and speed using the formula for kinetic energy: KE = 0.5 × m × v^2, where KE is kinetic energy, m is mass, and v is velocity. By rearranging this formula to solve for mass (m), we can determine the mass of the car. Substituting the given kinetic energy (3.0 × 10^5 J) and velocity (15 m/s) into the formula and solving for mass results in m = (2 × KE) / v^2. Plugging in the values: m = (2 × 3.0 × 10^5 J) / (15 m/s)^2 = (6.0 × 10^5 kg · m^2/s^2) / 225 m^2/s^2 = 2666.67 kg. Rounding to the nearest thousand gives us 3000 kg as the approximate mass of the car, which means none of the options given (a. 4000 kg, b. 5000 kg, c. 6000 kg, d. 7000 kg) are correct.
To find the mass of the car, we can use the equation for kinetic energy:
Kinetic energy = 0.5 * mass * velocity^2
Given that the car has a kinetic energy of 3.0 × 10^5 J and is traveling at 15 m/s, we can rearrange the equation and solve for mass:
Mass = (2 * kinetic energy) / velocity^2
Substituting the values, we get:
Mass = (2 * 3.0 × 10^5 J) / (15 m/s)^2
Mass = 4000 kg
Therefore, the mass of the car is 4000 kg, so the correct option is a. 4000 kg.