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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
Question 4
Two trains M and N are moving in the same direction along parallel straight horizontal tracks. At time t = 0, M overtakes N whilst they are travelling with speeds 40... show full transcript
Worked Solution & Example Answer: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
Step 1
Find the value of T.
Answer
To find T:
Use the distances traveled by both trains:
-
For Train N:
- Distance = Speed × Time = 30 m/s × 25 s = 750 m.
-
For Train M:
- Distance during T seconds = 40 m/s × T.
- Distance during deceleration (need to find this): Using the formula for distance during uniform deceleration: Distance = (Initial Speed + Final Speed)/2 × Time = (40 m/s + 0 m/s)/2 × t = 20 m/s × (t - T)
Where t is the total time taken by Train M to reach Y.
Set the total distances equal (since XY = 975 m):
egin{align*}
40T + 20(t - T) = 975
30T + 750 = 975
30T = 225
T = 7.5 ext{ seconds}.
\end{align*}
Thus, the value of T is 7.5 seconds.