Kinetic energy derivation, simple question

In summary, the book says to derive the kinetic energy by integration, while the text I am using says to derive the kinetic energy by taking the difference of the distance traveled and the time it took to travel that distance.
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Arman777
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I am trying to derive the kinetic energy from the work and can I derive it like this ?

$$W=\int Fdr$$
$$W=\int \frac {dp} {dt}dr=\int (dp) \frac {dr} {dt}=\int (mdv)v=1/2m[v_f^2-v_i^2]$$
 
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My book does this in 7 lines mine took 4. I don't know why books sometimes does things in long way.
 
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Arman777 said:
My book does this in 7 lines mine took 4. I don't know why books sometimes does things in long way.

Perhaps they prefer at least a modicum of mathematical rigour!
 
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Arman777 said:
My book does this in 7 lines mine took 4. I don't know why books sometimes does things in long way.
There's a bit of personal taste involved here; what one person considers admirable terseness another may consider skipping important steps.

With textbooks an additional consideration is that skipping steps can be a problem for a student who isn't already familiar with the concept. For example, someone taking intro physics concurrently with their first calculus course may have seen their first integral just a few weeks back - it's easy to imagine that your cavalier treatment of the bounds of integration would confuse them.

For what it's worth... I understand your derivation just fine but it's not what I'd be writing on a chalkboard in front of a class.
 
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Nugatory said:
There's a bit of personal taste involved here; what one person considers admirable terseness another may consider skipping important steps.

With textbooks an additional consideration is that skipping steps can be a problem for a student who isn't already familiar with the concept. For example, someone taking intro physics concurrently with their first calculus course may have seen their first integral just a few weeks back - it's easy to imagine that your cavalier treatment of the bounds of integration would confuse them.

For what it's worth... I understand your derivation just fine but it's not what I'd be writing on a chalkboard in front of a class.
Well yes you are right. Thanks for your reply
 

What is kinetic energy?

Kinetic energy is the energy an object possesses due to its motion.

How is kinetic energy calculated?

Kinetic energy is calculated using the formula KE = 1/2 * m * v^2, where m is the mass of the object and v is its velocity.

What is the derivation of kinetic energy?

The derivation of kinetic energy involves using the work-energy theorem, which states that the work done on an object is equal to the change in its kinetic energy. By integrating this equation, we can derive the formula for kinetic energy.

What is the difference between kinetic energy and potential energy?

Kinetic energy is the energy of motion, while potential energy is the energy that an object possesses due to its position or state. Kinetic energy can be converted into potential energy and vice versa.

What are some real-life examples of kinetic energy?

Some examples of kinetic energy include a moving car, a swinging pendulum, a flying airplane, and a rolling ball. Basically, any object or system that is in motion has kinetic energy.

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