Final answer:
To find the speed at which a car will have 5.0×10⁵ J of kinetic energy, the formula for kinetic energy KE = (1/2)mv² is used. Setting up a proportion between the initial and final kinetic energies and corresponding velocities, and solving for the new velocity, we find that the car needs to travel at approximately 18.0 m/s to reach the kinetic energy of 5.0×10⁵ J.
Step-by-step explanation:
To calculate at what speed the car will have 5.0×10⁵ J of kinetic energy after initially having 3.0×10⁵ J of kinetic energy at 14 m/s, we use the formula for kinetic energy KE = (1/2)mv², where m is the mass and v is the velocity of the car. Since the mass of the car remains consistent, we can set up a proportion between the initial and final kinetic energies and their corresponding velocities:
Initial KE = (1/2)mv² = 3.0×10⁵ J
Final KE = (1/2)mv² = 5.0×10⁵ J
Let's use the initial KE to find the mass of the car:
(1/2)m(14 m/s)² = 3.0×10⁵ J
m = (2 × 3.0×10⁵ J) / (14 m/s)²
Now, we can substitute this mass into the final KE equation to find the final velocity v for 5.0×10⁵ J:
(1/2)(2 × 3.0×10⁵ J / (14 m/s)²)v² = 5.0×10⁵ J
v² = (5.0×10⁵ J / 3.0×10⁵ J) × (14 m/s)²
v = sqrt((5.0×10⁵ J / 3.0×10⁵ J) × (14 m/s)²)
v ≈ 18.0 m/s
Therefore, the kinetic energy of 5.0×10⁵ J will be reached when the car is traveling at approximately 18.0 m/s.