Starting from rest a vehicle accelerates at the rate of 2~m/s^{2} towards east for 10 s. It then stops suddenly. It then accelerates again at a rate of 4\sqrt{2}m/s^{2} for next 10 s towards south and then again comes to rest. The net displacement of the vehicle from the starting point is

  1. A. 100 m
  2. B. 200 m
  3. C. 300 m ✓
  4. D. 400 m

Correct Answer: C. 300 m

Explanation

Distance towards east s_1 = \frac{1}{2}(2)(10)^2 = 100~m. Distance towards south s_2 = \frac{1}{2}(4\sqrt{2})(10)^2 = 200\sqrt{2}~m. Net displacement = \sqrt{s_1^2 + s_2^2} = \sqrt{100^2 + (200\sqrt{2})^2} = \sqrt{10000 + 80000} = \sqrt{90000} = 300~m.

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