Question

The speed of a train increases at a constant rate a from zero to v, and then remains constant for an interval,
and finally decreases to zero at a constant rate ß. If L be the total distance travelled, then the total time taken
is​

Answer 1

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