42. A car, starting from rest, has a constant
acceleration a, for a time interval t, during which
it covers a distances $1. In the next time intervaltz,
the car has a constant retardation a, and comes to
rest after covering a distance s2 in time tz. Which
of the following relations is correct?
acceleration a, for a time interval t, during which
it covers a distances $1. In the next time intervaltz,
the car has a constant retardation a, and comes to
rest after covering a distance s2 in time tz. Which
of the following relations is correct?
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Correct Question :
A car starting from rest has a constant acceleration a₁ for a time interval t₁ during which it covers a distances S₁. In the next time interval t₂ the car has a constant retardation a₂ and comes to rest after covering a distance S₂ in time interval t₂. Find the relation between distance, acceleration and time.
Solution :
⟩ Distance covered by car in case A :
➝ s₁ = (0 × t₁) + 1/2 (a₁ × t₁²)
➝ s₁ = a₁t₁² / 2 ___ [Eq. 1]
⟩ Final velocity after time t₁ :
➠ v₁ = 0 + a₁t₁
➠ v₁ = a₁t₁
⟩ Final velocity after time t₂ :
➠ 0 = a₁t₁ - a₂t₂
➠ a₁t₁ = a₂t₂ ___ [Eq. 2]
➠ t₁ / t₂ = a₂ / a₁ ___ [Eq
3]
⟩ Distance covered by car in case B :
➝ s₂ = (a₁t₁) t₂ - 1/2 (a₂ × t₂²)
From the second equation;
➝ s₂ = a₂t₂² - 1/2 a₂t₂²
➝ s₂ = 1/2 a₂t₂² ___ [Eq. 4]
From the first and fourth equation;
➙ s₁ / s₂ = (a₁t₁²/2) / (a₂t₂²/2)
From the third equation;
➙ s₁ / s₂ = (a₁ / a₂) × (a₂² / a₁²)
➙ s₁ / s₂ = a₂ / a₁ = t₁ / t₂
Answer:
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