The kinetic Energy (K)of a moving object varies jointly with it mass (m) and the square of it velocity (v)
If an object has a mass of 22.5 kilograms and moving with a velocity of 20 meters per second has a kinetic energy of 4500 joules, find it kinetic energy when the velocity is 32 meters per second.
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the subject is science
To solve this problem, we need to use the equation that describes the relationship between kinetic energy, mass, and velocity:
K = k * m * v^2
where:
K represents the kinetic energy
m represents the mass
v represents the velocity
k is a constant that represents the proportionality factor between K, m, and v
To find the value of k, we can rearrange the equation and solve for k:
k = K / (m * v^2)
Now that we have the value of k, we can substitute the given values of mass (m = 22.5 kg) and velocity (v = 20 m/s) into the equation and find the initial value of kinetic energy (K = 4500 J):
k = 4500 J / (22.5 kg * (20 m/s)^2)
k = 4500 J / (22.5 kg * 400 m^2/s^2)
k = 4500 J / (9000 kg*m^2/s^2)
k = 0.5 J/(kg*m^2/s^2)
Now that we know the value of k, we can use it to find the kinetic energy when the velocity is 32 m/s. We substitute the new value of velocity (v = 32 m/s) into the equation:
K = (0.5 J/(kg*m^2/s^2)) * 22.5 kg * (32 m/s)^2
K = (0.5 J/(kg*m^2/s^2)) * 22.5 kg * 1024 m^2/s^2
K = (0.5 J) * (22.5 kg) * (1024)
K = 11520 J
Therefore, when the velocity is 32 m/s, the object's kinetic energy is 11520 joules.