How do you get the velocity of a roller coaster when you are only given 250.0kg and 2.000x10^4 Joules
To determine the velocity of a roller coaster, you need to apply the principle of conservation of energy. This principle states that the total energy of a system remains constant if no external forces are acting on it.
In this case, you are given the mass of the roller coaster (250.0 kg) and the amount of energy (2.000x10^4 Joules). You can use this information to find the velocity.
The total energy of the roller coaster consists of its kinetic energy (related to its velocity) and its potential energy (related to its height above the ground). Since the roller coaster is on the ground, its potential energy can be ignored in this case.
The kinetic energy of an object can be calculated using the formula:
KE = (1/2) * mass * velocity^2
Given that KE is equal to 2.000x10^4 Joules and the mass is 250.0 kg, the equation becomes:
2.000x10^4 J = (1/2) * 250.0 kg * velocity^2
Now, rearrange the equation to solve for the velocity:
2.000x10^4 J = (1/2) * 250.0 kg * velocity^2
Divide both sides of the equation by (1/2) * 250.0 kg:
2.000x10^4 J / ((1/2) * 250.0 kg) = velocity^2
Simplify the equation:
2.000x10^4 J / (125.0 kg) = velocity^2
160 m^2/s^2 = velocity^2
Finally, take the square root of both sides to solve for the velocity:
velocity = √(160 m^2/s^2)
Therefore, the velocity of the roller coaster is approximately 12.65 m/s.