A 73 kg student traveling in acar with a constant velocity has a kinetic energy of 1.3 x 10^4 J. What is the speedometer reading of the car in km/h?
To solve this problem, we will use the equation for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
First, let's convert the student's mass from kilograms (kg) to grams (g) because the SI units for velocity are in meters per second (m/s) and kinetic energy is measured in joules (J).
73 kg = 73,000 g
Now, let's rearrange the formula to solve for velocity (v) by isolating it on one side:
2 * KE = mass * velocity^2
Divide both sides by the mass:
2 * KE / mass = velocity^2
Take the square root of both sides to solve for velocity:
√(2 * KE / mass) = velocity
Now, plug in the given values into the equation:
√(2 * 1.3 x 10^4 J / 73,000 g) = velocity
Perform the calculation:
√(26000 J / 73000 g) ≈ 0.347
The velocity of the car is approximately 0.347 m/s.
To find the speedometer reading in km/h, we need to convert meters per second (m/s) to kilometers per hour (km/h).
Multiply the velocity by a conversion factor of 3.6:
0.347 m/s * 3.6 km/h = 1.2492 km/h
Therefore, the speedometer reading of the car is approximately 1.25 km/h.