Question

A train starts from station A with uniform accleration ay and after some time it is retarded with retardation a₂ and travels some more distance. Altimately it stops at station B. The distance between A and B is 4 km and train takes a time of 4 min to cover this distance. It unit of acceleration be km/min 2 then prove that \(\frac{1}{a_1} + \frac{1}{a_2} = 2\)

Answer 1

Suppose time t₁ and t₂ is taken by train in two parts of journey and their distances are S₁ and S₂ respectively. According to question

S₁ + S₂ = 4 km ..........(1)

t₁ + t₂ = 4 min ...........(2)

For part AC, distance

S₁ = average velocity x time

From equation (1),

For part AC, from formula v = u + at

v = 0 + a₁t₁ ⇒ t₁ = \(\frac{v}{a_1} = \frac{2}{a_1}\) .............(5)

Similarly for part CB,

0 = v - a₂t₂ ⇒ t₂ = \(\frac{v}{a_2} = \frac{2}{a_2}\) ............(6)

∴ From equation (2),

\(\frac{2}{a_1} + \frac{2}{a_2} = 4\)