A Car Engine Supplies 2.0 x 10^4 J of Energy

Problem

A car engine supplies 2.0 x 10⁴ J of energy to the wheels. The car has a mass of 1000 kg and is initially at rest. What is the speed of the car after the engine supplies the energy?

Solution

1. Identify known variables:
   • Energy supplied by the engine: 2.0 x 10⁴ J
   • Mass of the car: 1000 kg
   • Initial velocity of the car: 0 m/s
2. Determine the final velocity of the car:
   • The energy supplied by the engine is converted into kinetic energy of the car:

   Kinetic energy = 1/2 * mass * velocity^2

   • Rearranging the equation to solve for velocity:

   Velocity = sqrt(2 * kinetic energy / mass)

   • Substituting the known values:

   Velocity = sqrt(2 * 2.0 x 10⁴ J / 1000 kg)

   Velocity = 14.14 m/s

Therefore, the speed of the car after the engine supplies the energy is 14.14 m/s.