To determine the increase in speed when the kinetic energy of a moving object increases by 96%, we need to understand the relationship between kinetic energy and speed.
The kinetic energy of an object is given by the formula:
KE = (1/2) * m * v^2
Where: KE = Kinetic Energy m = Mass of the object v = Velocity (speed) of the object
We can observe that the kinetic energy is directly proportional to the square of the velocity. Thus, if the kinetic energy increases by 96%, we can express it as:
New KE = Old KE + 96% of Old KE New KE = Old KE + 0.96 * Old KE New KE = 1.96 * Old KE
Since the kinetic energy is proportional to the square of the velocity, we can express the relationship as:
(1/2) * m * (New v)^2 = 1.96 * [(1/2) * m * (Old v)^2]
Canceling out the mass (m) on both sides, we have:
(New v)^2 = 1.96 * (Old v)^2
Taking the square root of both sides:
New v = √(1.96) * Old v
Now we can calculate the increase in speed by substituting the value of √(1.96) ≈ 1.4:
New v = 1.4 * Old v
Therefore, when the kinetic energy of a moving object increases by 96%, the speed will increase by approximately 40% (1.4 times the original speed).