Physics: Kinetic Energy The kinetic energy K of a moving...

Physics: Kinetic Energy The kinetic energy $K$ of a moving object varies jointly with its mass $m$ and the square of its velocity $v .$ If an object weighing 25 kilograms and moving with a velocity of 10 meters per second has a kinetic energy of 1250 joules, find its kinetic energy when the velocity is 15 meters per second.

Key Concepts

Joint Variation

Joint variation describes a relationship where a quantity depends on two or more other quantities simultaneously, often multiplied together. In physics, it is common to see formulas where a physical property is directly proportional to multiple factors, meaning any change in one or more factors proportionally affects the outcome.

Proportionality Constant

A proportionality constant is a fixed number that relates the variables in a joint variation or direct proportional equation. It serves as the multiplier that finalizes the relationship after the inherently adjustable variables are accounted for.

Kinetic Energy

Kinetic energy is a form of energy that a moving object possesses due to its mass and velocity. It is a central concept in physics, particularly in mechanics, and is fundamentally linked to the work required to accelerate an object to a certain speed.

Square Dependence

Square dependence indicates that a particular variable affects a quantity quadratically. In the context of kinetic energy, the velocity of an object is squared, which means that even small increases in velocity can result in significantly larger changes in kinetic energy.

Transcript

00:01 Okay, so good there everyone.

00:02 So we have here our problem, p6 kinetic energy.

00:06 So the kinetic energy k of a moving object varies jointly with its mass m and a square of its velocity v.

00:13 If an object weighing 25 kilograms and moving with a velocity of 10 meters per second and has a kinetic energy of 1 ,250 joules, find its kinetic energy when the velocity is 15 meters per second.

00:27 Okay, so the problem here is dealing with kinetic energy.

00:30 And we are dealing with a joint variation okay so first we will write our kinetic energy formula so k okay equals to and take note k of a moving object varies jointly with its mass and the square of its velocity so we can write it as various jointly of its mass and the square of its velocity v and the constant proportionality k okay so first we have here our given if an object weighing 25 kilograms so that is that would be our m so m is we can write it as m as 25 and a velocity of 10 meters per second so that would be our v then take note of the square and it has a kinetic energy of one thousand two 50 jol okay so the the first given signifies that we are dealing with our constant proportionality okay so we will simplify it 1 ,050 jol is equal to 25 times 100 okay because 10 squared is 100 times the constant proportionality okay so let's continue so 1 ,050 jol is equal to 250 times 100 is 2 ,500, okay, times our constant proportionality k.

02:20 So to solve 4k, we will divide both side by 25, okay, 25.

02:30 So our k here now will be, take note 25 divide 25 is 1 or canceled out.

02:37 So 1 ,250 divided by 2 ,500 is, so 25.

02:49 That would be one half...

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