A 64 kg student traveling in a car with a constant velocity has a kinetic energy of 1.6 10^4 J. What is the speedometer reading of the car in km/h?
(1/2) m v^2 = 1.6*10^4
32 v^2 = 160 * 10^2
v^2 = 5 * 10^2
v = 10 sqrt 5 or about 22.4 m/s
22.4 m/s *3600 s/h * 1 km/1000 m
= 80.5 km/h
To determine the speedometer reading of the car in km/h, we need to find the speed of the car.
The kinetic energy (KE) of an object is given by the formula: KE = (1/2) * mass * velocity^2.
In this case, the kinetic energy is given as 1.6 * 10^4 J, and the mass of the student is 64 kg.
So, we can rearrange the formula and solve for velocity:
velocity^2 = (2 * KE) / mass
Plugging in the values, we get:
velocity^2 = (2 * 1.6 * 10^4 J) / 64 kg
Simplifying further, we have:
velocity^2 = 50 * 10^2 J / kg
velocity^2 = 5000 J / kg
Now, to find the velocity, we take the square root of both sides of the equation:
velocity = √(5000 J / kg)
Calculating the square root, we get:
velocity ≈ 70.71 m/s
To convert this to km/h, we multiply by (3600 seconds/hour) and divide by 1000 meters/kilometer:
velocity ≈ (70.71 m/s * 3600 s/h) / (1000 m/km)
velocity ≈ 254.96 km/h
Therefore, the speedometer reading of the car is approximately 255 km/h.
To find the speedometer reading of the car, we can use the formula for kinetic energy:
Kinetic Energy = 1/2 * mass * velocity^2
Given:
Mass of the student (m) = 64 kg
Kinetic Energy (KE) = 1.6 * 10^4 J
We need to find the velocity.
1. Rearrange the formula for kinetic energy:
KE = 1/2 * m * v^2
2 * KE = m * v^2
2. Substitute the given values:
2 * (1.6 * 10^4 J) = (64 kg) * v^2
(3.2 * 10^4 J) = 64 kg * v^2
3. Divide both sides by 64 kg to isolate v^2:
(3.2 * 10^4 J) / 64 kg = v^2
5 * 10^2 J/kg = v^2
4. Take the square root of both sides to solve for v:
sqrt(5 * 10^2 J/kg) = v
sqrt(5 * 10^2 J/kg) ≈ 22.36 (approximated to two decimal places)
Therefore, the velocity (speed) of the car is approximately 22.36 m/s.
To convert the velocity from m/s to km/h, multiply it by 3.6 (1 m/s = 3.6 km/h):
22.36 m/s * 3.6 km/h = 80.5 km/h (rounded to one decimal place)
Hence, the speedometer reading of the car is approximately 80.5 km/h.