b) Deduce the expression for the distance travelled by a body moving with
uniform acceleration in a given time
Answers
Answer:
s
=
u
t
+
1
2
a
t
2
where
u
is initial velocity,
a
is uniform acceleration and
s
is the distance travelled by body in time
t
.
Second equation of motion gives distance travelled by a moving body in time
t
.
To obtain second equation of motion consider a body with initial velocity
u
moving with acceleration a for time
t
its final velocity at this time be
v
. If body covered distance
s
in this time
t
, then average velocity of the body would be
average velocity
Distance travelled by the body is
From first equation of motion
v
=
u
+
a
t
So putting first equation of motion in above equation we get ,
s
=
u
+
u
+
a
t
2
×
t
=
(
2
u
+
a
t
)
t
2
=
2
u
t
+
a
t
2
2
Rearranging it we get
s
=
u
t
+
1
2
a
t
2
Third equation of m
Explanation: