Final answer:
To find the speed of the car with 5.0 × 10⁵ J of kinetic energy, we can use the formula for kinetic energy and solve for the speed. The car will have a speed of approximately 50 m/s with 5.0 × 10⁵ J of kinetic energy. None of the option is correct.
Step-by-step explanation:
To find the speed of the car with 5.0 × 10⁵ J of kinetic energy, we can use the formula for kinetic energy: KE = 0.5 * m * v², where KE is the kinetic energy, m is the mass of the car, and v is the speed of the car.
Given that the car has 3.0 × 10⁵ J of kinetic energy at a speed of 15 m/s, we can calculate the mass of the car:
3.0 × 10⁵ = 0.5 * m * 15²
Solving for m:
m = (3.0 × 10⁵) / (0.5 * 15²)
m = 400 kg
Now, we can use the mass to find the speed of the car with 5.0 × 10⁵ J of kinetic energy:
5.0 × 10⁵ = 0.5 * 400 * v²
Solving for v:
v² = (5.0 × 10⁵) / (0.5 * 400)
v² = 2500
v = sqrt(2500)
v ≈ 50 m/s
Therefore, the car will have a speed of approximately 50 m/s with 5.0 × 10⁵ J of kinetic energy.