A particle is moving in a straight line with constant acceleration (a) it covers S1 distance in t time S2 distance in 2t and S3 in 3t. What is S1:S2:S3?
Answers
Answer:
Step-by-step explanation:
The particle started from rest at origin i.e u=0
Using s=ut+
2
at
2
where u=0
We get s
1
=
2
at
1
2
, s
2
=
2
at
2
2
and s
3
=
2
at
3
2
As s
1
, s
2
& s
3
are in GP ⟹ s
2
=
s
1
s
3
Also t
1
, t
2
& t
3
are in AP ⟹2t
2
=(t
1
+t
3
) and 2d=t
3
−t
1
Now RHS
d
2
(
s
1
−
s
3
)
2
=
d
2
s
1
+s
3
−2
s
1
s
3
=
d
2
s
1
+s
3
−2s
2
OR RHS =
2
a
×
d
2
t
1
2
+t
3
2
−2t
2
2
=
2
a
×
d
2
t
1
2
+t
3
2
−2×
4
(t
1
+t
3
)
2
OR RHS =
4d
2
a
×(t
3
−t
1
)
2
=
4d
2
a
×(2d)
2
⟹ RHS =a
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