Two trains A and B run on parallel straight tracks - Edexcel - A-Level Maths Mechanics - Question 7 - 2003 - Paper 1

To find the value of T, we can calculate the distances traveled by both trains until the point they meet:

1. Distance traveled by Train A:

   • During the first 12 seconds: ext{Distance}_A = rac{1}{2} a t^2 = rac{1}{2} imes rac{30 ext{ m/s}}{12 ext{ s}} imes (12 ext{ s})^2 = 180 ext{ m}
   • For the time after that until T, Train A travels at a constant speed: $ext{Distance}_A = 30 ext{ m/s} imes (T - 12) ext{ s}$

   So, total distance for Train A: $ext{Total}_A = 180 + 30(T - 12)$

2. Distance traveled by Train B:

   • Train B accelerates for 24 seconds after starting (from 40 s to 64 s): ext{Distance}_B = rac{1}{2} imes rac{60 ext{ m/s}}{24 ext{ s}} imes (24 ext{ s})^2 = 720 ext{ m}
   • After t = 64 seconds, it travels at constant speed: $ext{Constant Speed Distance} = 60 ext{ m/s} imes (T - 64) ext{ s}$

   So, total distance for Train B: $ext{Total}_B = 720 + 60(T - 64)$

3. Setting the distances equal for the time T: $180 + 30(T - 12) = 720 + 60(T - 64)$

   Expanding: $180 + 30T - 360 = 720 + 60T - 3840$

   Combining: $-30T + 180 + 360 + 3840 - 720 = 0$ $-30T + 3660 = 0$ $T = 122 ext{ seconds}$

After reviewing the graph provided earlier, we notice a calculation mistake; the final answer for T, based on inputs, should resolve to T = 98 seconds instead.