1
JEE Main 2020 (Online) 4th September Morning Slot
+4
-1
Starting from the origin at time t = 0, with initial velocity 5$$\widehat j$$ ms-1 , a particle moves in the x-y plane with a constant acceleration of $$\left( {10\widehat i + 4\widehat j} \right)$$ ms-2. At time t, its coordinates are (20 m, y0 m). The values of t and y0 are, respectively:
A
5s and 25 m
B
2s and 18 m
C
2s and 24 m
D
4s and 52 m
2
JEE Main 2020 (Online) 2nd September Morning Slot
+4
-1
Train A and train B are running on parallel tracks in the opposite directions with speeds of 36 km/hour and 72 km/hour, respectively. A person is walking in train A in the direction opposite to its motion with a speed of 1.8 km/ hour. Speed (in ms–1) of this person as observed from train B will be close to :
(take the distance between the tracks as negligible)
A
30.5 ms–1
B
29.5 ms–1
C
31.5 ms–1
D
28.5 ms–1
3
JEE Main 2020 (Online) 9th January Evening Slot
+4
-1
A particle starts from the origin at t = 0 with an
initial velocity of 3.0 $$\widehat i$$ m/s and moves in the
x-y plane with a constant acceleration $$\left( {6\widehat i + 4\widehat j} \right)$$ m/s2 . The x-coordinate of the particle at the instant when its y-coordinate is 32 m is D meters. The value of D is :-
A
40
B
32
C
50
D
60
4
JEE Main 2020 (Online) 8th January Evening Slot
+4
-1
A particle moves such that its position vector $$\overrightarrow r \left( t \right) = \cos \omega t\widehat i + \sin \omega t\widehat j$$ where $$\omega$$ is a constant and t is time. Then which of the following statements is true for the velocity $$\overrightarrow v \left( t \right)$$ and acceleration $$\overrightarrow a \left( t \right)$$ of the particle :
A
$$\overrightarrow v$$ and $$\overrightarrow a$$ both are perpendicular to $$\overrightarrow r$$
B
$$\overrightarrow v$$ and $$\overrightarrow a$$ both are parallel to $$\overrightarrow r$$
C
$$\overrightarrow v$$ is perpendicular to $$\overrightarrow r$$ and $$\overrightarrow a$$ is directed towards the origin
D
$$\overrightarrow v$$ is perpendicular to $$\overrightarrow r$$ and $$\overrightarrow a$$ is directed away from the origin
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