4. Two trains M and N are moving in the same direction along parallel straight horizontal tracks - Edexcel - A-Level Maths Mechanics - Question 4 - 2016 - Paper 1

To find the value of T, we can use the equations of motion:

1. For Train N:

   The distance travelled by N in 25 seconds is given by:

   $ext{Distance} = ext{Speed} \times ext{Time} = 30 \times 25 = 750 ext{ m}$

   The remaining distance from X to Y is:

   $XY - 750 = 975 - 750 = 225 ext{ m}$

   For the deceleration of N, with uniform deceleration where final speed = 0, we can use the relation:

   $s = ut + \frac{1}{2}at^2$

   Let t_1 be the time taken to decelerate after 25 seconds, we know:

   $225 = 30t_1 + \frac{1}{2}(-a)t_1^2$

2. For Train M:

   The distance travelled by M is given by:

   $ext{Distance} = 40T + \frac{1}{2}(-a_M)(t_M)^2$

   Setting this equal to 975 m and combining equations:

   Substituting and solving, we can find:

   $T = 8.75 ext{ seconds (or } \frac{35}{4} ext{ s)}$