Class 9 motion all formulas
Answers
Explanation:
Motion
Equation of Motion:
Relation among velocity, distance, time and acceleration is called equations of motion. There are three equations of motion:
First Equation of Motion:
The final velocity (v) of a moving object with uniform acceleration (a) after time, t.
Let, the initial velocity = u.
Final velocity = v.
Time = t
Acceleration = a
We know that, Acceleration (a)
=
Change in velocity
Time taken
⇒
a
=
Final velocity-Initial velocity
Time taken
⇒
a
=
v
−
u
t
⇒
a
t
=
v
−
u
⇒
a
t
−
v
=
−
u
⇒
−
v
=
−
u
−
a
t
⇒
v
=
u
+
a
t
---(i)
This equation is known as first equation of motion.
Second Equation of Motion:
Distance covered in time (t) by a moving body.
Let, Initial velocity of the object = u
Final velocity of the object = v
Acceleration = a
Time = t
Distance covered in given time = s
We know that,
Average velocity
=
Initial velocity+Final velocity
2
∴ Average velocity
=
u
+
v
2
----(ii)
We know that, Distance covered (s) in given time = Average velocity x Time
Or, s = Average velocity x Time -----------------(iii)
After substituting the value of average velocity from equation (ii) we get
⇒
s
=
u
+
v
2
×
t
After substituting the value of ‘v’ from first equation of motion we get,
⇒
s
=
u
+
(
u
+
a
t
)
2
×
t
⇒
s
=
u
+
u
+
a
t
2
×
t
⇒
s
=
2
u
+
a
t
2
×
t
⇒
s
=
2
u
t
+
a
t
2
2
⇒
s
=
2
u
t
2
+
a
t
2
2
⇒
s
=
u
t
+
a
t
2
2
⇒
s
=
u
t
+
1
2
a
t
2
----(iv)
The above equation is known as Second equation of motion.
Third Equation of Motion:
The third equation of motion is derived by substituting the value of time (t) from first equation of motion.
We know from first equation of motion,
v
=
u
+
a
t
⇒
v
−
u
=
a
t
⇒
a
t
=
v
−
u
⇒
t
=
v
−
u
a
-----(v)
We know that the second equation of motion is,
s
=
u
t
+
1
2
a
t
2
By substituting the value of
t
from euqation (v) we get
s
=
u
(
v
−
u
a
)
+
1
2
a
(
v
−
u
a
)
2
⇒
s
=
u
×
v
−
u
a
+
1
2
a
(
v
−
u
)
2
a
2
⇒
s
=
u
(
v
−
u
)
a
+
a
×
(
v
−
u
)
2
2
×
a
×
a
⇒
s
=
u
v
−
u
2
a
+
(
v
−
u
)
2
2
a
⇒
s
=
2
(
u
v
−
u
2
)
+
(
v
−
u
)
2
2
a
⇒
2
a
s
=
2
u
v
−
2
u
2
+
v
2
+
u
2
−
2
u
v
⇒
2
a
s
=
−
2
u
2
+
v
2
+
u
2
⇒
2
a
s
=
−
u
2
+
v
2
⇒
2
a
s
+
u
2
=
v
2
⇒
v
2
=
u
2
+
2
a
s
---(vi)
This is called the Third equation of motion.
Answer:
there in tb
Explanation: yes