Show that the kinetic energy of an object can be written in terms of the momentum as
KE = p2/2m.
Help ASAP please. Step by step to get the answer
I will be happy to critique your thinking. I am getting the impression you are answer grazing.
I just want to see if I got the step by step correct
To show that the kinetic energy (KE) of an object can be written in terms of its momentum (p) as KE = p^2/2m, we can follow these steps:
Step 1: Start with the definition of momentum.
Momentum (p) is defined as the product of an object's mass (m) and its velocity (v):
p = m * v
Step 2: Express velocity in terms of momentum and mass.
Rearrange the momentum equation to solve for velocity:
v = p / m
Step 3: Substitute the expression for velocity into the kinetic energy formula.
The kinetic energy (KE) is given by the equation:
KE = (1/2) * m * v^2
Substitute the expression for velocity (v) from Step 2 into the KE equation:
KE = (1/2) * m * (p / m)^2
Simplify the equation:
KE = (1/2) * m * (p^2 / m^2)
Step 4: Cancel out the common factor of 'm' in the numerator and denominator.
Since 'm' appears in both the numerator and denominator, cancel it out:
KE = (1/2) * p^2 / m
Step 5: Simplify further to obtain the desired result.
Divide the numerator by 2 to simplify the equation:
KE = p^2 / 2m
Therefore, we have shown that the kinetic energy (KE) of an object can be written in terms of its momentum (p) as KE = p^2/2m.