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Kinematics-1D

585 Questions Start Allen Test
All Exams Allen Advance Errorless
JEE (Main) June 2022 Q26 Errorless Critical Thinking MCQ
When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is
A.
19.6 m
B.
29.4 m
C.
39.2 m
D.
73.5 m
JEE (Main) June 2022 Q27 Errorless Critical Thinking MCQ
An object of mass 5kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to [Use $g = 10 ms^{-2}$ ]
A.
1:1
B.
$\sqrt{2} : \sqrt{3}$
C.
$\sqrt{3} : \sqrt{2}$
D.
2:3
JEE (Main) June 2022 Q28 Errorless Critical Thinking MCQ
An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero
A.
Momentum
B.
Potential energy
C.
Acceleration
D.
Force
JEE (Main) June 2022 Q29 Errorless Critical Thinking MCQ
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
A.
10 m
B.
20 m
C.
30 m
D.
40 m
JEE (Main) June 2022 Q30 Errorless Critical Thinking MCQ
Two buses $P$ and $Q$ start from a point at the same time and move in a straight line and their positions are represented by $X_{P}(t) = \alpha t + \beta t^{2}$ and $X_{Q}(t) = ft - t^{2}$ . At what time, both the buses have same velocity
A.
$\frac{\alpha - f}{1 + \beta}$
B.
$\frac{\alpha + f}{2(\beta - 1)}$
C.
$\frac{\alpha + f}{2(1 + \beta)}$
D.
$\frac{f - \alpha}{2(1 + \beta)}$
JEE (Main) June 2022 Q31 Errorless Critical Thinking MCQ
Velocity(v) and acceleration (a) in two systems of units 1 and 2 are related as $v_{2} = \frac{n}{m^{2}} v_{1}$ and $a_{2} = \frac{a_{1}}{mn}$ respectively. Here m and n are constants. The relations for distance and time in two systems respectively are
A.
$\frac{n^{3}}{m^{3}} L_{1} = L_{2}$ and $\frac{n^{2}}{m} T_{1} = T_{2}$
B.
$L_{1} = \frac{n^{4}}{m^{2}} L_{2}$ and $T_{1} = \frac{n^{2}}{m} T_{2}$
C.
$L_{1} = \frac{n^{2}}{m} L_{2}$ and $T_{1} = \frac{n^{4}}{m^{2}} T_{2}$
D.
$\frac{n^{2}}{m} L_{1} = L_{2}$ and $\frac{n^{4}}{m^{2}} T_{1} = T_{2}$
JEE (Main) June 2022 Q32 Errorless Critical Thinking MCQ
Two balls A and B are placed at the top of 180 m tall tower. Ball A is released from the top at t = 0 s. Ball B is thrown vertically down with an initial velocity ā€˜uā€™ at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of ā€˜uā€™ in $ms^{-1}$ [use $g = 10 ms^{-2}$ ]
A.
10
B.
15
C.
20
D.
30
JEE (Main) July 2022 Q33 Errorless Critical Thinking MCQ
At time t=0 a particle starts travelling from a height $7\hat{z}$ cm in a plane keeping z coordinate constant. At any instant of time it's position along the $\hat{x}$ and $\hat{y}$ directions are defined as 3t and $5t^{3}$ respectively. At t=1s acceleration of the particle will be
A.
$-30\hat{y}$
B.
$30\hat{y}$
C.
$3\hat{x} + 15\hat{y}$
D.
$3\hat{x} + 15\hat{y} + 7\hat{z}$
JEE (Main) July 2022 Q34 Errorless Critical Thinking MCQ
A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is
A.
g/2n
B.
g/n
C.
2gn
D.
g/2nĀ²
JEE (Main) July 2022 Q35 Errorless Critical Thinking MCQ
A NCC parade is going at a uniform speed of 9 km/h under a mango tree on which a monkey is sitting at a height of 19.6 m. At any particular instant, the monkey drops a mango. A cadet will receive the mango whose distance from the tree at time of drop is (Given $g = 9.8 \, m/s^{2}$ )
A.
5 m
B.
10 m
C.
19.8 m
D.
24.5 m
JEE (Main) July 2022 Q36 Errorless Critical Thinking MCQ
A ball is released from a height h. If $t_{1}$ and $t_{2}$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_{1}$ and $t_{2}$
A.
$t_{1} = (\sqrt{2})t_{2}$
B.
$t_{1} = (\sqrt{2} - 1)t_{2}$
C.
$t_{2} = (\sqrt{2} + 1)t_{1}$
D.
$t_{2} = (\sqrt{2} - 1)t_{1}$
JEE (Main) June 2022, Jan. 2023 Q37 Errorless Critical Thinking MCQ
An object moves with speed $v_{1}, v_{2}$ and $v_{3}$ along a line segment AB, BC and CD respectively as shown in figure. Where AB = BC and AD = 3 AB, then average speed of the object will be
A.
$\frac{(v_1 + v_2 + v_3)}{3}$
B.
$\frac{v_1v_2v_3}{3(v_1v_2 + v_2v_3 + v_3v_1)}$
C.
$\frac{3v_1v_2v_3}{v_1v_2 + v_2v_3 + v_3v_1}$
D.
$\frac{(v_1 + v_2 + v_3)}{3v_1v_2v_3}$
JEE-Main 2021 Q38 Allen JEE-Main PYQs MCQ
The velocity-displacement graph describing the motion of a bicycle is shown in the figure. The acceleration-displacement graph of the bicycle's motion is best described by :
A.
B.
C.
D.
JEE-Main 2021 Q39 Allen JEE-Main PYQs MCQ
The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by :
A.


B.


C.


D.


JEE-Main 2021 Q40 Allen JEE-Main PYQs MCQ
Water droplets are coming from an open tap at a particular rate. The spacing between a droplet observed at $4^{th}$ second after its fall to the next droplet is 34.3 m. At what rate the droplets are coming from the tap? (Take $g = 9.8 \, m/s^{2}$ )
A.
3 drops / 2 seconds
B.
2 drops / second
C.
1 drop / second
D.
1 drop / 7 seconds
JEE-Main 2021 Q41 Allen JEE-Main PYQs MCQ
A ball is thrown up with a certain velocity so that it reaches a height 'h'. Find the ratio of the two different times of the ball reaching $\frac{h}{3}$ in both the directions.
A.
$\frac{\sqrt{2}-1}{\sqrt{2}+1}$
B.
$\frac{1}{3}$
C.
$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$
D.
$\frac{\sqrt{3}-1}{\sqrt{3}+1}$
JEE-Main 2021 Q42 Allen JEE-Main PYQs MCQ
A butterfly is flying with a velocity $4\sqrt{2}$ m/s in North-East direction. Wind is slowly blowing at 1 m/s from North to South. The resultant displacement of the butterfly in 3 seconds is:
A.
3 m
B.
20 m
C.
$12\sqrt{2}m$
D.
15 m
JEE-Main 2021 Q43 Allen JEE-Main PYQs Numerical
A swimmer wants to cross a river from point A to point B. Line AB makes an angle of $30^{\circ}$ with the flow of river. Magnitude of velocity of the swimmer is same as that of the river. The angle $\theta$ with the line AB should be ____Ā°, so that the swimmer reaches point B.
JEE (Main) Feb. 2021 Q44 Errorless Critical Thinking MCQ
A stone is dropped from the top of a building. When it crosses a point 5 m below the top, another stone starts to fall from a point 25 m below the top. Both stones reach the bottom of building simultaneously. The height of the building is
A.
35 m
B.
45 m
C.
50 m
D.
25 m
JEE (Main) Feb. 2021 Q45 Errorless Critical Thinking MCQ
A scooter accelerates from rest for time $t_1$ at constant rate $a_1$ and then retards at constant rate $a_2$ for time $t_2$ and comes to rest. The correct value of $\frac{t_1}{t_2}$ will be
A.
$\frac{a_1 + a_2}{a_2}$
B.
$\frac{a_2}{a_1}$
C.
$\frac{a_1}{a_2}$
D.
$\frac{a_1 + a_2}{a_1}$
JEE (Main) March 2021 Q46 Errorless Critical Thinking MCQ
A rubber ball is released from a height of 5m above the floor. It bounces back repeatedly, always rising to $\frac{81}{100}$ of the height through which it falls. Find the average speed of the ball (Take $g = 10 ms^{-2}$ )
A.
$3.0 ms^{-1}$
B.
$3.50 ms^{-1}$
C.
$2.0 ms^{-1}$
D.
$2.50 ms^{-1}$
JEE (Main) July 2021 Q47 Errorless Critical Thinking MCQ
The relation between time t and distance x for a moving body is given as $t = mx^{2} + nx$ , where m and n are constants. The retardation of the motion is (When v stands for velocity)
A.
$2mv^{3}$
B.
$2mnv^{3}$
C.
$2nv^{3}$
D.
$2n^{2}v^{3}$
JEE (Main) July 2021 Q48 Errorless Critical Thinking MCQ
The instantaneous velocity of a particle moving in a straight line is given as $v = \alpha t + \beta t^2$ , where $\alpha$ and $\beta$ are constants. The distance travelled by the particle between 1s and 2s is
A.
$3\alpha + 7\beta$
B.
$\frac{3}{2}\alpha + \frac{7}{3}\beta$
C.
$\frac{\alpha}{2} + \frac{\beta}{3}$
D.
$\frac{3}{2}\alpha + \frac{7}{2}\beta$
JEE (Main) July 2021 Q49 Errorless Critical Thinking MCQ
A balloon was moving upwards with a uniform velocity of 10 m/s. An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around (takes the value of g as $10m/s^{2}$ )
A.
300 m
B.
200 m
C.
125 m
D.
250 m
JEE (Main) July 2021, 22 Q50 Errorless Critical Thinking MCQ
A ball is thrown up vertically with a certain velocity so that, it reaches a maximum height h. Find the ratio of the times in which it is at height $\frac{h}{3}$ while going up and coming down respectively
A.
$\frac{\sqrt{2}-1}{\sqrt{2}+1}$
B.
$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$
C.
$\frac{\sqrt{3}-1}{\sqrt{3}+1}$
D.
$\frac{1}{3}$