1
JEE Main 2024 (Online) 30th January Morning Shift
Numerical
+4
-1

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.

2
JEE Main 2024 (Online) 27th January Evening Shift
Numerical
+4
-1

A body falling under gravity covers two points $$A$$ and $$B$$ separated by $$80 \mathrm{~m}$$ in $$2 \mathrm{~s}$$. The distance of upper point A from the starting point is _________ $$\mathrm{m}$$ (use $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$).

3
JEE Main 2023 (Online) 1st February Evening Shift
Numerical
+4
-1

For a train engine moving with speed of $$20 \mathrm{~ms}^{-1}$$, the driver must apply brakes at a distance of 500 $$\mathrm{m}$$ 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 $$\sqrt{x} \mathrm{~ms}^{-1}$$. The value of $$x$$ is ____________.

(Assuming same retardation is produced by brakes)

4
JEE Main 2023 (Online) 30th January Morning Shift
Numerical
+4
-1

A horse rider covers half the distance with $$5 \mathrm{~m} / \mathrm{s}$$ speed. The remaining part of the distance was travelled with speed $$10 \mathrm{~m} / \mathrm{s}$$ for half the time and with speed $$15 \mathrm{~m} / \mathrm{s}$$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $$\frac{x}{7} \mathrm{~m} / \mathrm{s}$$. The value of $$x$$ is ___________.