Question

6. A train starts from rest from a station with
acceleration 0.2 m/s2 on a straight track and then
comes to rest after attaining maximum speed on
another station due to retardation 0.4 m/s2. If total
time spent is half an hour, then distance between
two stations is [Neglect length of train]
in (1) 216 km
(2) 512 km
(3) 728 km
(4) 1296 km​

Answer 1

Explanation:

Given,

Velocity v

1

achieve in time t

1

,due to acceleration, a

1

=0.2ms

−2

v

1

=u

1

+at

1

⇒v

1

=0+0.2t

1

Velocity reduce to zero in time t

2

, due to retardation, a

2

=−0.4ms

−2

v

2

=v

1

+at

2

⇒0=v

1

−0.4t

2

Add time

t

1

+t

2

=

0.2

v

1

+

0.4

v

1

⇒30×60=v

1

×7.5

⇒v

1

=240m/s

Apply kinematic equation

v

2

−u

2

=2as

s=

2a

v

2

−u

2

Total distance S

1

+S

2

=

2a

1

v

1

2

+

2a

2

v

1

2

=

2×0.2

240

2

+

2×0.4

240

2

=216km