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Kinematics-1D

182 Questions Start Errorless Test
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JEE (Main) June 2022 Q26 Errorless 6. 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 Q27 Errorless 6. 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 ‘u’ at t = 2 s. After a certain time, both balls meet 100 m above the ground. Find the value of ‘u’ in $ms^{-1}$ [use $g = 10 ms^{-2}$ ]
A.
10
B.
15
C.
20
D.
30
JEE (Main) July 2022 Q28 Errorless 6. 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 Q29 Errorless 6. 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/2n²
JEE (Main) July 2022 Q30 Errorless 6. 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 Q31 Errorless 6. 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 Q32 Errorless 6. 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) Feb. 2021 Q33 Errorless 6. 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 Q34 Errorless 6. 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 Q35 Errorless 6. 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 Q36 Errorless 6. 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 Q37 Errorless 6. 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 Q38 Errorless 6. 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 Q39 Errorless 6. 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.
$\frac{1}{3}$
JEE (Main) July 2021 Q40 Errorless 6. Critical Thinking 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) Aug. 2021 Q41 Errorless 6. Critical Thinking MCQ
A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a
A.
Hyperbola
B.
Straight line vertically down the plane
C.
Parabola in a direction opposite to the motion of plane
D.
Parabola in the direction of motion of plane
JEE (Main) Aug. 2021 Q42 Errorless 6. Critical Thinking MCQ
Water drops are falling from a nozzle of a shower onto the floor from a height of 9.8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor
A.
2.94 m
B.
4.18 m
C.
2.45 m
D.
7.35 m
JEE (Main) Aug. 2021 Q43 Errorless 6. Critical Thinking MCQ
A huge circular arc of length 4.4 ly subtends an angle 4s at the centre of circle. How long it would take for a body to complete 4 revolution if its speed is 8 AU per second (Given: $1ly = 9.46 \times 10^{15} m$ , $1AU = 1.5 \times 10^{11} m$ )
A.
$4.1 \times 10^{8} s$
B.
$4.5 \times 10^{10} s$
C.
$7.2 \times 10^{8} s$
D.
$3.5 \times 10^{6} s$
JEE (Main) March 2021 Q44 Errorless 7. Graphical Questions MCQ
The velocity-displacement graph of a particle is shown in the figure The acceleration-displacement graph of the same particle is represented by
A.
B.
C.
D.
JEE (Main) March 2021 Q45 Errorless 7. Graphical Questions MCQ
The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by
A.


B.


C.


D.


JEE (Main) March 2021 Q46 Errorless 7. Graphical Questions 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) Feb. 2021 Q47 Errorless 7. Graphical Questions MCQ
If the velocity-time graph has the shape AMB, what would be the shape of the corresponding acceleration-time graph
A.
B.
C.
D.
JEE (Main) Jan. 2020 Q48 Errorless 6. Critical Thinking MCQ
Train A and train B are running on parallel tracks in the opposite directions with speed 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 $^{-1}$
JEE (Main) Sep. 2020 Q49 Errorless 6. Critical Thinking MCQ
Starting from the origin at time t=0, with initial velocity $5\hat{j}ms^{-1}$ , a particle moves in the x-y plane with a constant acceleration of $(10\hat{i}+4\hat{j})ms^{-2}$ . At time t, its coordinates are $(20\ m,\ y_{0}m)$ . The values of t and $y_{0}$ , are respectively
A.
4s and 52 m
B.
2s and 24 m
C.
2s and 18 m
D.
5s and 25 m
JEE (Main) Sep. 2020 Q50 Errorless 6. Critical Thinking MCQ
A helicopter rises from rest on the ground vertically upwards with a constant acceleration g. A food packet is dropped from the helicopter when it is a height h. The time taken by the packet to reach the ground is close to [g is the acceleration due to gravity]
A.
$t = \sqrt{\frac{2h}{3g}}$
B.
$t = 1.8\sqrt{\frac{h}{g}}$
C.
$t = 3.4\sqrt{\left(\frac{h}{g}\right)}$
D.
$t = \frac{2}{3}\sqrt{\left(\frac{h}{g}\right)}$