Uniformly Accelerated Motion PYQs: JEE Mains Physics

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1. 1. A particle starts moving from time \(t=0\) and its coordinate is given as \(x(t)=4t^{3}-3t.\)
   A. The particle returns to its original position (origin) 0.866 units later
   B. The particle is 1 unit away from origin at its turning point.
   C. Acceleration of the particle is non-negative.
   D. The particle is 0.5 units away from origin at its turning point.
   E. Particle never turns back as acceleration is non-negative.
   Choose the correct answer from the options given below : 2026 Hard
2. 2. Two masses of \(3.4\) kg and \(2.5\) kg are accelerated from an initial speed of \(5\) m/s and \(12\) m/s, respectively. The distances traversed by the masses in the \(5^\text{th}\) second are \(104\) m and \(129\) m, respectively. The ratio of their momenta after \(10\) s is \(\dfrac{x}{8}\). The value of \(x\) is ________. 2026 Hard
3. 3. A bus moving along a straight highway with speed of \(72 \mathrm{~km} / \mathrm{h}\) is brought to halt within \(4 \mathrm{~s}\) after applying the brakes. The distance travelled by the bus during this time (Assume the retardation is uniform) is __________\(\mathrm{m}\). 2024 Hard
4. 4. A particle starts with an initial velocity of \(10.0\,ms ^{-1}\) along \(x\)-direction and accelerates uniformly at the rate of \(2.0\,ms ^{-2}\). The time taken by the particle to reach the velocity of \(60.0\,ms ^{-1}\) is \(.......\,s\) 2023 Easy
5. 5. For a train engine moving with speed of \(20 \;ms ^{-1}\). the driver must apply brakes at a distance of \(500 \;m\) before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed \(\sqrt{ x }\; ms ^{-1}\). The value of \(x\) is \(..............\) (Assuming same retardation is produced by brakes) 2023 Medium
6. 6. A particle is moving in a straight line such that its velocity is increasing at \(5\,ms ^{-1}\) per meter. The acceleration of the particle is \(ms ^{-2}\) at a point where its velocity is \(20\,ms ^{-1}\). 2022 Medium
7. 7. A small toy starts moving from the position of rest under a constant acceleration. If it travels a distance of \(10 \,m\) in \(t \;s ,\) the distance travelled by the toy in the next \(t s\) will be .........\(m\) 2022 Medium
8. 8. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity \(u\) and the last compartment with velocity \(v\). The velocity with which middle point of the train passes the signal post is 2021 Medium
9. 9. If the velocity of a body related to displacement \({x}\) is given by \(v=\sqrt{5000+24 {x}} \;{m} / {s}\), then the acceleration of the body is \(\ldots \ldots {m} / {s}^{2}\) 2021 Hard
10. 10. An automobile, travelling at \(40\, km/h\), can be stopped at a distance of \(40\, m\) by applying brakes. If the same automobile is travelling at \(80\, km/h\), the minimum stopping distance, in metres, is (assume no skidding)..........\(m\) 2018 Medium

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