A 68 kg student traveling in a car with a constant velocity has a kinetic energy of 1.5 104 J. What is the speedometer reading of the car in km/h?
To find the speedometer reading of the car in km/h, we need to use the formula for kinetic energy:
Kinetic Energy (KE) = (1/2) * mass * velocity^2
We are given the following information:
Mass (m) = 68 kg
Kinetic Energy (KE) = 1.5 * 10^4 J
We need to solve for velocity (v).
Rearranging the formula, we get:
velocity^2 = (2 * KE) / mass
Substituting the given values, we have:
velocity^2 = (2 * 1.5 * 10^4) / 68
Simplifying further:
velocity^2 = 4411.76
Taking the square root of both sides:
velocity = √4411.76
velocity ≈ 66.43 m/s
Now, we need to convert the velocity from m/s to km/h.
To convert m/s to km/h, we need to remember that 1 km = 1000 m and 1 hour = 3600 seconds.
So, 1 m/s = (1 km / 1000 m) * (3600 s / 1 hour) = 3.6 km/h
Multiplying the velocity by the conversion factor:
velocity in km/h ≈ 66.43 m/s * 3.6 km/h
velocity in km/h ≈ 239.15 km/h
Therefore, the speedometer reading of the car is approximately 239.15 km/h.
To find the speedometer reading of the car, we can use the equation for kinetic energy:
Kinetic energy = (1/2) * mass * speed^2
Given:
Mass of student (m) = 68 kg
Kinetic energy (KE) = 1.5 * 10^4 J
Rearranging the equation, we can solve for speed (v):
Speed^2 = (2 * KE) / m
Plugging in the given values:
Speed^2 = (2 * 1.5 * 10^4) / 68
Simplifying:
Speed^2 = (3 * 10^4) / 68
Speed^2 ≈ 441.1765
Taking the square root of both sides:
Speed ≈ √441.1765
Speed ≈ 21.0 m/s
To convert this speed to km/h:
Speed = (21.0 m/s) * (3600 s/h) / (1000 m/km)
Speed ≈ 75.6 km/h
Therefore, the speedometer reading of the car would be approximately 75.6 km/h.