Question

Calculate the relativistic kinetic energy of a 1000-kg car moving at 30.0 m/s if the speed of light were only 45.0 m/s.

a)2.5 x 10^6 J
b)5.0 x 10^6 J
c)7.5 x 10^6 J
d)1.0 x 10^7 J

Answer 1

The relativistic kinetic energy of the car is approximately 7.5 x 10^6 J.

Step-by-step explanation:

To calculate the relativistic kinetic energy of the car, we can use the formula:

KE = (γ - 1) * mc^2

Where: KE is the kinetic energy, γ is the Lorentz factor given by γ = 1 / √(1 - v^2/c^2), m is the mass of the car, c is the speed of light, and v is the velocity of the car.

Plugging in the values, we have:

KE = (1 / √(1 - (30.0 m/s)^2 / (45.0 m/s)^2) - 1) * (1000 kg) * (45.0 m/s)^2

Simplifying the expression, we find that the relativistic kinetic energy of the car is approximately 7.5 x 10^6 J.