1
JEE Main 2024 (Online) 1st February Evening Shift
Numerical
+4
-1
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A particle initially at rest starts moving from reference point $x=0$ along $x$-axis, with velocity $v$ that varies as $v=4 \sqrt{x} \mathrm{~m} / \mathrm{s}$. The acceleration of the particle is __________ $\mathrm{ms}^{-2}$.
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2
JEE Main 2024 (Online) 1st February Morning Shift
Numerical
+4
-1
Change Language
A particle is moving in one dimension (along $x$ axis) under the action of a variable force. It's initial position was $16 \mathrm{~m}$ right of origin. The variation of its position $(x)$ with time $(t)$ is given as $x=-3 t^3+18 t^2+16 t$, where $x$ is in $\mathrm{m}$ and $\mathrm{t}$ is in $\mathrm{s}$.

The velocity of the particle when its acceleration becomes zero is _________ $\mathrm{m} / \mathrm{s}$.
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3
JEE Main 2024 (Online) 30th January Morning Shift
Numerical
+4
-1
Change Language

The displacement and the increase in the velocity of a moving particle in the time interval of $$t$$ to $$(t+1) \mathrm{s}$$ are $$125 \mathrm{~m}$$ and $$50 \mathrm{~m} / \mathrm{s}$$, respectively. The distance travelled by the particle in $$(\mathrm{t}+2)^{\mathrm{th}} \mathrm{s}$$ is _________ m.

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4
JEE Main 2024 (Online) 29th January Morning Shift
Numerical
+4
-1
Change Language

A ball rolls off the top of a stairway with horizontal velocity $$u$$. The steps are $$0.1 \mathrm{~m}$$ high and $$0.1 \mathrm{~m}$$ wide. The minimum velocity $$u$$ with which that ball just hits the step 5 of the stairway will be $$\sqrt{x} \mathrm{~ms}^{-1}$$ where $$x=$$ __________ [use $$\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$$ ].

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