Question

(ii) Derive formula for Kinetic energy​

Answer 1

Kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity.

Derivation:

Let us consider an object of m which is at rest lying on a table.

Let A force F acts on the object which moves the object through a distance S.

The workdone=F×S

W=F

net

×S-------(1)

Let the work done on the object causes a change in its velocity from u to V and let a be the acceleration.

From Third equation of motion:

V²−u²=2as

s=V²−u²/2a----------(2)

By Newton's Second law:

F=ma------(3)

From equation (1), (2) and (3)

W=ma×(V

2

−u

2

/2a)=(1/2)m(V

2

−u

2

)

As we assumed object at rest, u=0

W=(1/2)mV

2

we know that the kinetic energy of a body moving with a certain velocity is equal to work done on the object to acquire that velocity from rest.

∴K.E=1/2mV

$\huge\underbrace\mathcal\red{⬆⬆ANSWER⬆⬆}$

Answer 2

Answer:

$\LARGE{\underline{\underline{\green{\bf{Required\:answer:}}}}}$

⇝The third kinematic formula can be derived by plugging in the first kinematic formula, v = v 0 + a t v=v_0+at v=v0+atv, equals, v, start subscript, 0, end subscript, plus, a, t, into the second kinematic formula, Δ x t = v + v 0 2 \dfrac{\Delta x}{t}=\dfrac{v+v_0}{2} tΔx=2v+v0.

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