Physics

Problem

Two stations

S_1

and

S_2

are

1.0\,\text{km}

apart on a straight track. At the instant a train

A

starts from rest at

S_1

with a uniform acceleration of

0.5\,\text{m s}^{-2}

towards

S_2

, another train

B

passes station

S_2

moving towards

S_1

20\,\text{m s}^{-1}

. Train

B

immediately applies brakes and decelerates uniformly at

1.0\,\text{m s}^{-2}

. a. (i) Calculate the time taken after the start of train

A

for the two trains to meet. b. (ii) Determine how far from station

S_1

the meeting point is located. c. (iii) Find the speed of each train at the instant they meet.