a 60-kg student travelling in a 1000 kg car with a constant velocity has a kinetic energy of 1.2 *10^4 J. What is the speedometer reading of the car in km/h?
KE = 0.5*M*V^2 = 12,000 J.
0.5*60*V^2 = 12000.
V = 20 m/s.
Speed = 0.020km/s * 3600s/h = 72 km/h.
To find the speedometer reading of the car in km/h, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given:
Mass of the student (m1) = 60 kg
Mass of the car (m2) = 1000 kg
Total mass (m) = m1 + m2 = 60 kg + 1000 kg = 1060 kg
Kinetic Energy (KE) = 1.2 * 10^4 J
Since the student and the car have a constant velocity, their combined kinetic energy is equal to the kinetic energy of the car alone.
Therefore, we can write the equation as:
KE of car = (1/2) * total mass * velocity^2
1.2 * 10^4 J = (1/2) * 1060 kg * velocity^2
Simplifying:
2 * 1.2 * 10^4 J / 1060 kg = velocity^2
Rearranging the equation:
velocity^2 = 2 * 1.2 * 10^4 J / 1060 kg
Taking the square root of both sides:
velocity = √(2 * 1.2 * 10^4 J / 1060 kg)
Using a calculator:
velocity ≈ 9.35 m/s
To convert this velocity from m/s to km/h, we multiply by 3.6 (1 hour = 3600 seconds):
velocity ≈ 9.35 m/s * 3.6 ≈ 33.6 km/h
Therefore, the speedometer reading of the car is approximately 33.6 km/h.