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 `t` is

For the first phase (0 to t seconds): Initial velocity (u₁) = 0, acceleration (a₁) = 2 m/s². Distance s₁ = u₁t + (1/2)a₁t² = 0t + (1/2)2t² = t². Velocity at time t (v₁) = u₁ + a₁t = 0 + 2t = 2t m/s. For the second phase (t to t+10 seconds): Initial velocity (u₂) = v₁ = 2t m/s, acceleration (a₂) = 5 m/s², time (t₂) = 10 s. Distance s₂ = u₂t₂ + (1/2)a₂t₂² = (2t)10 + (1/2)5(10)² = 20t + 250 m. Total distance = s₁ + s₂ = t² + 20t + 250. Given total distance is 550 m, t² + 20t + 250 = 550, which simplifies to t² + 20t - 300 = 0. Factoring the quadratic: (t + 30)(t - 10) = 0. Possible solutions are t = -30 or t = 10. Since time cannot be negative, t = 10 s.