At what speed must a 950 kg subcompact car be moving to have the same kinetic energy as a 3.2*10^4 kg truck going 20 km/h ?
1/2mv^2=1/2mv^2
v(subcompact)= 116.0762 km/h
To find the speed at which the subcompact car must be moving, in order to have the same kinetic energy as the truck, we can equate the kinetic energies of both objects.
The formula for kinetic energy is:
KE = (1/2) * m * v^2
Where KE is the kinetic energy, m is the mass of the object, and v is the velocity.
Given:
Mass of the subcompact car (m1) = 950 kg
Mass of the truck (m2) = 3.2 * 10^4 kg
Velocity of the truck (v2) = 20 km/h
First, let's convert the velocity of the truck from km/h to m/s:
20 km/h * (1000 m/1 km) * (1 h / 3600 s) = 5.56 m/s
Now, let's calculate the kinetic energy of the truck:
KE2 = (1/2) * m2 * v2^2
KE2 = (1/2) * (3.2 * 10^4 kg) * (5.56 m/s)^2
Now, we can equate the kinetic energies and solve for the velocity of the subcompact car (v1):
KE1 = KE2
(1/2) * m1 * v1^2 = (1/2) * m2 * v2^2
Simplifying the equation:
(m1 / m2) * v1^2 = v2^2
Substituting the given values:
(950 kg / (3.2 * 10^4 kg)) * v1^2 = (5.56 m/s)^2
Now, solve for v1:
v1^2 = [(5.56 m/s)^2 * (3.2 * 10^4 kg)] / 950 kg
v1^2 = 309.4916 m^2/s^2
Taking the square root of both sides:
v1 = √309.4916 m^2/s^2
v1 ≈ 17.59 m/s
Therefore, the subcompact car must be moving at a speed of approximately 17.59 m/s to have the same kinetic energy as the truck.
To find the speed at which the 950 kg car must be moving to have the same kinetic energy as the 32,000 kg truck going 20 km/h, we need to consider the formula for kinetic energy:
Kinetic Energy (KE) = 1/2 * mass * velocity^2
In this case, we know the mass of the car (950 kg) and the velocity of the truck (20 km/h). Let's convert the velocity of the truck to meters per second (m/s) before proceeding with the calculation.
1 km/h = 0.2778 m/s (approximately)
20 km/h = 0.2778 * 20 = 5.56 m/s (approximately)
Now, let's calculate the kinetic energy of the truck:
KE(truck) = 1/2 * mass(truck) * velocity(truck)^2
= 1/2 * 32,000 kg * (5.56 m/s)^2
Next, let's calculate the kinetic energy of the car:
KE(car) = 1/2 * mass(car) * velocity(car)^2
Since the question is asking for the speed of the car, we need to isolate the velocity(car) term by equating the kinetic energies of the car and the truck:
KE(truck) = KE(car)
1/2 * 32,000 kg * (5.56 m/s)^2 = 1/2 * 950 kg * velocity(car)^2
Simplify the equation:
velocity(car)^2 = (32,000 kg / 950 kg) * (5.56 m/s)^2
velocity(car)^2 = 184.147...
Finally, take the square root of both sides to find the velocity(car):
velocity(car) = √(184.147...)
velocity(car) ≈ 13.56 m/s
Therefore, the 950 kg car must be moving at approximately 13.56 m/s to have the same kinetic energy as the 32,000 kg truck going 20 km/h.