NDA 2 2024 GAT, question 91

Topic: Physics

Q91

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

(a) $10\text{ s}$ Correct answer
(b) $13\text{ s}$
(c) $20\text{ s}$
(d) $25\text{ s}$

Solution.

Answer: (a) $10\text{ s}$

During the first stage, distance s₁=½×2×t²=t² and final speed is 2t.
During the next 10 s, s₂=(2t)10+½×5×10²=20t+250.
Thus t²+20t+250=550, or (t−10)(t+30)=0.
Reject negative time: t=10 s.