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

  1. A. 10 s ✓
  2. B. 13 s
  3. C. 20 s
  4. D. 25 s

Correct Answer: A. 10 s

Explanation

Distance in first t seconds = \frac{1}{2}(2)t^2 = t^2. Velocity after t seconds = 2t. Distance in next 10 seconds = (2t)(10) + \frac{1}{2}(5)(10)^2 = 20t + 250. Total distance t^2 + 20t + 250 = 550 \Rightarrow t^2 + 20t - 300 = 0 \Rightarrow t = 10~s.

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