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Motion in a Straight Line
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Acceleration
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The relation between time t and distance
Question
The relation between time t and distance x is
t
=
a
x
2
+
b
x
where a and b are constants.The acceleration is
A
−
2
a
v
3
B
2
a
v
2
C
−
2
a
v
2
D
2
b
v
3
Easy
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Solution
Verified by Toppr
Correct option is A)
t
=
a
x
2
+
b
x
Differentiate w.r.t time
1
=
2
a
x
d
t
d
x
+
b
d
t
d
x
d
t
d
x
=
2
a
x
+
b
1
V
=
2
a
x
+
b
1
...(1)
a
=
d
t
d
V
=
(
2
a
x
+
b
)
2
−
(
2
a
d
t
d
x
)
a
=
(
2
a
x
+
b
)
2
−
2
a
v
....(2)
Substiting
2
a
x
+
b
1
=
V
in (2)
we will get,
a
=
−
2
a
v
3
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