Question

The two ends of a train moving with a constant acceleration pass a certain point with velocities u
and v. Find the velocity with which the middle point of the train passes the same point​

Answer 1

Answer :

The two ends of a train moving with a constant acceleration pass a certain point with velocities u and v.

We have to find the velocity with which the middle point of the train passes the same point$.$

Let s be the total distance between points P and Q and x be the velocity of train while passing a certain middle point of PQ.

If a is the acceleration of the car, then

1) For part PQ,

→ v² - u² = 2as

→ a = (v² - u²) / 2s __ (i)

2) For part RQ,

→ v² - x² = 2a(s/2)

→ v² - x² = as

→ a = (v² - x²) / s __ (ii)

From equation (i) and (ii)...

→ (v² - u²) / 2 = v² - x²

→ v² - u² = 2v² - 2x²

→ 2x² = v² - u²

→ x² = (v² - u²) / 2

→ x = √[ (v² - u²) / 2 ]