A vehicle starts moving along a straight line path from rest. In first t seconds it moves with an acceleration of 2 m/s2 and then in next 10 seconds it moves with an acceleration of 5 m/s2. The total distance travelled by the vehicle is 550 m. The value of time is

Correct option is A

In the first t seconds, the vehicle's initial velocity is 0, and the acceleration is 2 m/s². The distance covered in the first phase: S₁ = (1/2) × a₁ × t² = (1/2) × 2 × t² = t² In the second phase, the acceleration is 5 m/s² for the next 10 seconds. The initial velocity for the second phase, v1v₁v1​, will be the velocity at the end of the first phase. v₁ = a₁ × t = 2t Now, the distance covered in the second phase: S₂ = v₁ × t₂ + (1/2) × a₂ × t₂² S₂ = (2t) × 10 + (1/2) × 5 × 10² S₂ = 20t + 250 Total distance = S₁ + S₂ = 550 meters => t² + 20t + 250 = 550 => t² + 20t - 300 = 0 Solving this quadratic equation: t = 10 seconds ∴ The value of time is 10 seconds. Correct answer: (a) 10 seconds