explain the third low of motion by graphical method
Answers
Explanation:
The distance covered by the object moving with uniform acceleration is given by the area of trapezium ABDO
Therefore, Area of trapezium ABDOE
=12×(sum of parallel sides+distance between parallel sides)=12×(sum of parallel sides+distance between parallel sides)
⇒ Distance(s)=12(DO+BE)×OE=12(DO+BE)×OE⇒s=12(u+v)×t⇒s=12(u+v)×t ----(iii)
Now from equation (ii) a=v−uta=v-ut
∴t=v−ut∴t=v-ut ----(iv)After substituting the value of
t
t from equation (iv) in equation (iii)
⇒s=12(u+v)×(v−u)a⇒s=12(u+v)×(v-u)a
⇒
s
=
1
2
a
(
v
+
u
)
(
v
−
u
)
⇒s=12a(v+u)(v-u)
⇒
2
a
s
=
(
v
+
u
)
(
v
−
u
)
⇒2as=(v+u)(v-u)
⇒
2
a
s
=
v
2
−
u
2
⇒2as=v2-u2
⇒
2
a
s
+
u
2
=
v
2
⇒2as+u2=v2
⇒
v
2
=
u
2
+
2
a
s
⇒v2=u2+2as
The above expression gives the relation between position and velocity and is called the third equation of motion.
While solving the problems related to velocity, distance, time and acceleration following three points should be considered: