The speed of a train at a constant rate α from zero to v and then remains constant for an interval and finally decreases to zero at a constant rate β . if Life be the total distance travelled then the total time taken is
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Explanation:
ANSWER
v=αt
1
⇒t
1
=
α
v
v=βt
1
⇒t
2
=
β
v
∴t
0
=t−t
1
−t
2
=(t−
α
v
−
β
v
)
Now,l=
2
1
αt
1
2
+vt
0
+
2
1
βt
2
1
⇒
2
1
α(
α
v
)
2
+v(t−
α
v
−
β
v
)+
2
1
β(
β
v
)
2
⇒vt−
2α
v
2
−
2β
v
2
⇒t=
v
l
+
2
v
(
α
1
+
β
1
)
For t to be minimum its first derivative with respect to velocity should be zero or,
⇒0=−
v
2
l
+
2αβ
α+β
⇒v=
α+β
2lαβ
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