Question

Two stations P and Q are 5.2 km apart. A train starts from rest at the station P and

accelerates uniformly to attain a speed of 54km/h in 30 seconds. The speed is

maintained until the brakes are applied. The train comes to rest at the station Q with

uniform retardation of 1m/s2

. Determine the total time required to cover the distance

between these two stations​

Answer 1

Answer:

Solution

For first 15s

v=u+at [I

st

eq

n

of motion]

⇒v=(0)+2×15

v=30m/s

when train is decelerating

v

′

=u

′

+a

′

t

′

⇒(0)=(30)−

2

1

t

′

⇒t

′

=60s

In first case

v

2

−u

2

=2as

1

[3

rd

eq

n

of motion]

(30)

2

−(0)=2(2)s

1

225m=s

1

In third case

(0)

2

−(30)

2

=2(−1/2)s

3

⇒900=s

3

So, in second case when

speed is constant :

s

2

=2000−s

1

+s

2

s

2

=2000−900−225

s

2

=875m

s

2

=vt

′′

t

′′

=

v

s

2

=

30

875

=29.16s

solution