Final answer:
The kinetic energies are (a) 5 × 10^6 J, (b) 400 J, and (c) 1.1 × 10^−14 J.
Step-by-step explanation:
The kinetic energy of an object can be calculated using the formula KE = 1/2mv^2, where KE is the kinetic energy, m is the mass of the object, and v is the velocity of the object.
Using this formula, we can calculate the kinetic energies:
(a) KE = 1/2(2000.0 kg)(100.0 km/h)^2 = 5 × 10^6 J
(b) KE = 1/2(80.0 kg)(10. m/s)^2 = 400 J
(c) KE = 1/2(9.1×10^−31 kg)(2.0×10^7 m/s)^2 = 1.1 × 10^−14 J
Calculating Kinetic Energies
To calculate the kinetic energy (KE) of objects in motion, we will use the formula KE = 1/2 m v^2, where m is the mass of the object and v is the velocity. The mass should be in kilograms (kg) and the velocity in meters per second (m/s).
(a) An automobile: The mass is 2000.0 kg and the velocity is 100.0 km/h, which needs to be converted to meters per second by multiplying by (1000 m / 1 km) × (1 h / 3600 s), resulting in a velocity of 27.78 m/s. Hence, KE = 1/2 × 2000.0 × (27.78)^2 = 5 × 10^5 J.
(b) A runner: With a mass of 80.0 kg and a velocity of 10.0 m/s, the kinetic energy can be calculated as KE = 1/2 × 80 × (10)^2 = 4000 J.
(c) An electron: The mass of the electron is 9.1×10⁻³¹-kg and the velocity is given as 2.0×10⁷ m/s. The kinetic energy is KE = 1/2 × 9.1×10⁻³¹⁻ kg × (2.0×10⁷ m/s)^2 = 1.1 × 10⁻¹⁴ J.
The correct option that represents the calculated kinetic energies is (a) 5 × 10^5 J, 4,000 J, 1.1 × 10⁻¹⁴ J.