Answer:
answer below
Explanation:
Let the initial velocity of the object be u. Let an external force be applied on it so that gets displaced by distance s and its velocity becomes v. In this scenario, the kinetic energy of the moving body is equal to the work that was required to change its velocity from u to v.
thus, we have the velocity- position relation as:
V
2
=u
2
+2as
or
s=
2a
v
2
−u
2
....(i)
Where, a is the acceleration of the during the change in its velocity. Now, the work done on the body by the external force is given by:
W=F×s
F = ma ... (ii)
from equations (i) and (ii), we obtain :
W=ma×(
2a
v
2
−u
2
)=
2
1
m(v
2
−u
2
)
If the body was initially at rest 9 i. e, u = 0 ), then :
W=
2
1
mv
2
Since kinetic energy is equal to the work done on the body to change its velocity from 0 to v , we obtain: kinetic energy , E
k
=
2
1
mv
2