Question

If a body moving with uniform acceleration in a straight line describes successive equal distances in time intervals (T1, T2, T3) respectively. Then prove

1 / T1 + 1 / T2 + 1 / T3 = 3 / T1 + T2 + T3​

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Answer 1

Answer :-

1 / T₁ - 1 / T₂ + 1 / T₃ = 3 / (T₁ +T₂ + T₃ )

Explanation :-

Let say Velocities,

V₀ , V₁ , V₂ & V₃ at T₀ , T₁ , T₁ + T₂ & T₁ + T₂ + T₃ Respectively.

As Body is moving with Uniform Acceleration,

s = (V₀ + V₁)T₁/2

→ s = (V₁ + V₂)T₂/2

→ s = (V₂ + V₃)T₃/2

→ 3s = (V₀ + V₃)(T₁+T₂+T₃)/2

→ V₀ + V₃ = 6s/(T₁+T₂+T₃)

→ V₀ + V₃ =  (V₀ + V₁) - (V₁ + V₂) + (V₂ + V₃)

→ V₀ + V₃ = 2s/T₁ - 2s/T₂ + 2s/T₃

→ 2s/T₁ - 2s/T₂ + 2s/T₃ =  6s/(T₁+T₂+T₃)

→ 1/T₁ - 1/T₂ + 1/T₃ = 3/(T₁+T₂+T₃)

Thanks ...

Answer 2

Refer to the Attachment.

Hope it Helps !!!!!