NDA 2 2024 GAT, question 98

Topic: Physics

Q98

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

(a) $100\text{ m}$
(b) $200\text{ m}$
(c) $300\text{ m}$ Correct answer
(d) $400\text{ m}$

Solution.

Answer: (c) $300\text{ m}$

Each stage begins from rest.
Eastward distance=½×2×10²=100 m; southward distance=½×4√2×10²=200√2 m.
The perpendicular components give displacement √[100²+(200√2)²]=300 m.
The idealised sudden stops add no distance.