Please help me solve this problem the kinetic energy (k) energy of a moving object with varies jointy with it mass (m) and the squareo of its velocity (v). If an object has an mass of 22.5 kilograms and moving with a velocity of 20 meters per secomd has a kinetic energy energy of 4500 joules, find it kinetic energy when the velocity is 32 meters per second.
Please help me write me write a 250 word summary of the above problem written work should include an explanation of the problem, a review of the mathematical concept involved a critque of method used to obtain the solution, and an interperation of the answer. Can someone help me please
To solve this problem, we need to use the formula for kinetic energy, which is given by:
k = 1/2 * m * v^2
Where k is the kinetic energy, m is the mass, and v is the velocity of the object.
In this case, we are given that the mass (m) is 22.5 kilograms and the velocity (v) is 20 meters per second. We are also given that the kinetic energy (k) is 4500 joules.
Substituting these values into the formula, we get:
4500 = 1/2 * 22.5 * (20^2)
We can solve this equation to find the value of v^2:
4500 = 1/2 * 22.5 * 400
4500 = 9000
v^2 = 4500 / (1/2 * 22.5)
v^2 = 200
Now, we need to find the kinetic energy when the velocity is 32 meters per second. We can substitute the new velocity value into the equation:
k = 1/2 * 22.5 * (32^2)
Calculating this equation, we get:
k = 1/2 * 22.5 * 1024
k = 11520 joules
So, when the velocity is 32 meters per second, the kinetic energy of the object is 11520 joules.
In a 250-word summary, you can explain the problem as finding the kinetic energy of an object based on its mass and velocity using the formula. Discuss the concept of kinetic energy and how it is influenced by mass and velocity. Analyze the method used to solve the problem, highlighting the substitution of values into the formula and the algebraic manipulation. Finally, interpret the answer in terms of the kinetic energy at a different velocity, emphasizing the increase in kinetic energy as the velocity increases due to the square factor in the formula.