Q19) a) Derive an equation for position -time relationship for a body moving with uniform acceleration.
Answers
Answer:
Derivation for the equation of Potenstial Energy:
Let the work done on the object against gravity = W
Work done, W = force × displacement
Work done, W = mg × h
Work done, W = mgh
Since workdone on the object is equal to mgh, an energy equal to mgh units is gained by the object . This is the potential energy (Ep) of the object.
Ep = mgh
Derivation for the equation of Kinetic Energy:
The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is
v2 - u2 = 2aS
This gives
S =
v
2
-
u
2
2a
We know F = ma. Thus using above equations, we can write the workdone by the force, F as
W = ma
×
(
v
2
-
u
2
2a
)
or
W =
1
2
m(
v
2
-
u
2
)
If object is starting from its stationary position, that is, u = 0, then
W =
1
2
m
v
2
It is clear that the work done is equal to the change in the kinetic energy of an object.
If u = 0, the work done will be
W =
1
2
m
v
2
.
Thus, the kinetic energy possessed by an object of mass, m and moving with a uniform velocity, v is Ek = ½ mv2
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Amna javeed
You must see in the CBSE science book for class 9th. The derivation of these two expressions are clearly given.
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Syeda
Answer.
Derivation for the equation of Potenstial Energy:
Let the work done on the object against gravity = W
Work done, W = force × displacement
Work done, W = mg × h
Work done, W = mgh
Since workdone on the object is equal to mgh, an energy equal to mgh units is gained by the object . This is the potential energy (Ep) of the object.
Ep = mgh
Derivation for the equation of Kinetic Energy:
The relation connecting the initial velocity (u) and final velocity (v) of an object moving with a uniform acceleration a, and the displacement, S is
v2 - u2 = 2aS
This gives
Explanation:
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