A student is traveling in a car with a constant velocity has a kinetic energy 1.0 x 10^4 J. What is the speedometer reading of the car in km/h.
To find the speedometer reading of the car in km/h, we first need to correlate the kinetic energy with the velocity of the car. The kinetic energy (KE) of an object is given by the formula:
KE = 0.5 * mass * velocity^2
Since the question states that the car is traveling with a constant velocity, we can assume it is at a constant speed, and therefore acceleration is zero. We can disregard the mass of the car since it is not provided and it cancels out in the equation. Hence, we have:
KE = 0.5 * velocity^2
Now let's rearrange the equation to solve for velocity:
velocity^2 = (2 * KE) / 1
velocity^2 = 2 * KE
Taking the square root of both sides, we get:
velocity = sqrt(2 * KE)
Plugging in the given kinetic energy:
velocity = sqrt(2 * 1.0 x 10^4 J)
Calculating this value:
velocity ≈ sqrt(2 * 10,000 J)
velocity ≈ sqrt(20,000 J)
velocity ≈ 141.42 m/s
Now, to convert the velocity from meters per second (m/s) to kilometers per hour (km/h), we need to multiply by the conversion factor of 3.6 (since 1 km = 1000 m and 1 hour = 3600 seconds):
velocity_km_per_hour ≈ 141.42 m/s * (3.6 km/h) / (1 m/s)
velocity_km_per_hour ≈ 509.11 km/h
Therefore, the speedometer reading of the car would be approximately 509.11 km/h.