Question

pls explain this expression
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Answer 1

Explanation:

Here W is Work done which is also Energy.

Work Done (W) = Force ( F ) × Displacement ( s or x or any variable)

Deriving an equation by substituting displacement 's' with the 3rd equation of motion, v² - u² = 2as, which is expressed with relation to displacement as

s = (v² - u²)/ 2a

Now W = F × s,

Force again can be derived as F = ma

( According to Newton's 2nd Law of Motion)

Expanding both F and s, we get work done

W = ma × (v² - u²)/ 2a

( acceleration would cancel out. because 2a is denominator)

Now we get the equation W = m(v² - u²)/ 2

As we are considering Kinetic Energy, the initial point or u

is considered as 0. Here we take only final point or position.

Then, W = m(v² - 0²)/ 2 or m×v² × 1/2

More precisely, W = 1/2 (mv²)

Work is Energy. So W can also be expressed as KE (Kinetic Energy)

Then KE = 1/2 (mv²)

Answer 2

Answer:

The kinetic energy of an object is the energy an object has due to its motion. The formula for kinetic energy is:

KE=1/2 mv^2 , where m is the object’s mass and v is its velocity.

This formula is derived from the work-energy theorem, which states that the amount of work done on an object is equal to the change in its energy. Assuming potential energy is constant, Work is equal to the change in kinetic energy. This is expressed in the formula ∆KE=Fd. You can then use algebra or calculus to derive the kinetic energy equation.

Algebra Derivation:

∆KE=Fd

∆KE=mad (recall that F=ma)

Now, we use the kinematic equation: vf^2-vi^2= 2ad and solve for ad, then we substitute into the original equation.

∆KE=m((vf^2-vi^2)/2)

(vf is final velocity and vi is initial velocity)

We finally expand to get:

∆KE=1/2 mvf^2–1/2mvi^2

This is one of the countless ways to derive the kinetic energy theorem.

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