Question

derive the formula of kinetic energy plz solve it fast

Answer 1

To derive the equation I used a system where a particle starts at rest, and then has a constant force applied to it so that it accelerates with a constant acceleration. At time t=T
t
=
T
the particle has velocity v
v
, acceleration a
a
, kinetic energy Ek
E
k
, mass m
m
and a force F
F
being applied on it.

F=ma
F
=
m
a
F=mΔvΔt=m(v−0)Δt=mvΔt
F
=
m
Δ
v
Δ
t
=
m
(
v
−
0
)
Δ
t
=
m
v
Δ
t
FΔt=mv
F
Δ
t
=
m
v

Work must be done on the particle for it to have kinetic energy.

ΔEk=FΔd
Δ
E
k
=
F
Δ
d
F=ΔEkΔd
F
=
Δ
E
k
Δ
d

Combining the two equations:

ΔEk ΔtΔd=mv
Δ
E
k

Δ
t
Δ
d
=
m
v
ΔEkv=mv
Δ
E
k
v
=
m
v
Ek−0=mv2
E
k
−
0
=
m
v
2
Ek=mv2
E
k
=
m
v
2

Answer 2

may it helps uhh.....