A car is moving at 50 miles per hour. The kinetic energy of that car is 5 × 105 J.
How much energy does the same car have when it moves at 114 miles per hour?
Answer in units of J
2599200
To calculate the energy the car has when it moves at 114 miles per hour, we can use the formula for kinetic energy:
Kinetic Energy = (1/2) * mass * velocity^2
Given that the kinetic energy of the car when it moves at 50 miles per hour is 5 × 10^5 J, we can use this information to solve for the mass of the car.
5 × 10^5 J = (1/2) * mass * (50 mph)^2
Simplifying the equation:
5 × 10^5 J = (1/2) * mass * 2500 mph^2
mass = (5 × 10^5 J) / (1250 mph^2)
mass = 400 kg (approximation)
Now, we can calculate the energy the car has when it moves at 114 miles per hour using the same formula:
Kinetic Energy = (1/2) * mass * velocity^2
Kinetic Energy = (1/2) * 400 kg * (114 mph)^2
Kinetic Energy = 1/2 * 400 * 12996
Kinetic Energy = 2599200 J
Therefore, the energy the same car has when it moves at 114 miles per hour is 2,599,200 J.
To find the energy of the car when it moves at 114 miles per hour, we can use the formula for kinetic energy:
Kinetic energy (KE) = 1/2 * mass * velocity^2
To solve this problem, we need to make an assumption that the mass of the car remains constant.
Given:
Initial velocity (v1) = 50 miles per hour
Initial kinetic energy (KE1) = 5 × 10^5 J
We can calculate the initial kinetic energy using the formula above:
KE1 = 1/2 * mass * (v1)^2
Rearranging the formula, we can solve for mass:
mass = KE1 / (1/2 * (v1)^2)
Substituting the given values, we get:
mass = 5 × 10^5 J / (1/2 * (50 miles per hour)^2)
mass = 5 × 10^5 J / (1/2 * 50^2 miles^2/hour^2)
mass = 5 × 10^5 J / (1/2 * 2500 miles^2/hour^2)
mass = 5 × 10^5 J / (1250 miles^2/hour^2)
mass = 400 J/mile^2 * hour^2
Now that we have determined the mass of the car, we can find the kinetic energy of the car when it moves at 114 miles per hour.
New velocity (v2) = 114 miles per hour
Using the formula for kinetic energy, we can calculate the energy:
KE2 = 1/2 * mass * (v2)^2
Substituting the mass and velocity values, we get:
KE2 = 1/2 * (400 J/mile^2 * hour^2) * (114 miles per hour)^2
Simplifying the equation:
KE2 = 1/2 * (400 J/mile^2 * hour^2) * (114^2 miles^2/hour^2)
KE2 = 200 J/mile^2 * hour^2 * 12996 miles^2/hour^2
KE2 = 2,599,200 J/mile^2 * hour^2
Therefore, the energy of the car when it moves at 114 miles per hour is approximately 2,599,200 Joules (J).
Kinetic energy is proportional to mass and also varies with the square of the velocity.
So the new kinetic energy
=(5*105 joules)*(114/50)²