STD 11 - Motion in straight line PYQs: JEE Mains Physics – Page 2

Showing 51–100 of 102 questions

51. 51. The distance travelled by an object in time \(t\) is given by \(s =(2 \cdot 5) t ^2\). The instantaneous speed of the object at \(t =5\,s\) will be \(....\,ms ^{-1}\) 2023 Easy
52. 52. The position of a particle related to time is given by \(x =\left(5 t ^2-4 t +5\right) m\). The magnitude of velocity of the particle at \(t=2\,s\) will be \(...........ms^{-1}\) 2023 Easy
53. 53. The position-time graphs for two students \(A\) and \(B\) returning from the school to their homes are shown in figure \((A)\) \(A\) lives closer to the school \((B)\) \(B\) lives closer to the school \((C)\) \(A\) takes lesser time to reach home \((D)\) \(A\) travels faster than \(B\) \((E)\) \(B\) travels faster than \(A\) Choose the correct answer from the options given below :
    2023 Medium
54. 54. The velocity time graph of a body moving in a straight line is shown in figure.The ratio of displacement to distance travelled by the body in time \(0\) to \(10\,s\) is
    2023 Medium
55. 55. Two trains ' \(A\) ' and ' \(B\) ' of length ' \(l\) ' and ' \(4 l\) ' are travelling into a tunnel of length ' \(L\) ' in parallel tracks from opposite directions with velocities \(108\,km / h\) and \(72\,km / h\), respectively. If train '\(A\)' takes \(35\,s\) less time than train ' \(B\) ' to cross the tunnel then, length ' \(L\) ' of tunnel is \(...........\,m\) \(\text { (Given } L=60 l \text { ) }\) 2023 Medium
56. 56. A ball is projected vertically upward with an initial velocity of \(50 \; ms ^{-1}\) at \(t =0 \; s\). At \(t =2 \,s\). another ball is projected vertically upward with same velocity. At \(t= \; \dots \; s\), second ball will meet the first ball \(\left( g =10 \; ms ^{-2}\right)\). 2022 Hard
57. 57. 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 \(t_{2}\). 2022 Hard
58. 58. 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. 2022 Hard
59. 59. A ball is thrown vertically upwards with a velocity of \(19.6\,ms ^{-1}\) from the top of a tower. The ball strikes the ground after \(6\,s\). The height from the ground up to which the ball can rise will be \(\left(\frac{ k }{5}\right) m .\) The value of \(k\) is ..... (use \(g =9.8\,m / s ^{2}\)) 2022 Hard
60. 60. A ball of mass \(0.5 \; kg\) is dropped from the height of \(10 \; m\). The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is \(\dots \; m\). (Use \(g =10 \; m / s ^{2}\)). 2022 Medium
61. 61. A car covers \(A B\) distance with first one-third at velocity \(v _{1} ms ^{-1}\), second one-third at \(v _{2} ms ^{-1}\) and last one-third at \(v _{3} ms ^{-1}\). If \(v _{3}=3 v _{1}, v _{2}=2 v _{1}\) and \(v _{1}=11\,ms ^{-1}\) then the average velocity of the car is________ \(ms ^{-1} .\)
    2022 Medium
62. 62. A car is moving with speed of \(150\,km / h\) and after applying the brake it will move \(27\,m\) before it stops. If the same car is moving with a speed of one third the reported speed then it will stop after travelling \(....m\) distance. 2022 Medium
63. 63. 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 2022 Medium
64. 64. A particle is moving in a straight line such that its velocity is increasing at \(5\,ms ^{-1}\) per meter. The acceleration of the particle is \(ms ^{-2}\) at a point where its velocity is \(20\,ms ^{-1}\). 2022 Medium
65. 65. 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 .........\(m\) 2022 Medium
66. 66. From the top of a tower, a ball is thrown vertically upward which reaches the ground in \(6 \,s\). A second ball thrown vertically downward from the same position with the same speed reaches the ground in \(1.5\, s\). A third ball released, from the rest from the same location, will reach the ground in........ \(s\). 2022 Hard
67. 67. If \(t =\sqrt{ x }+4\), then \(\left(\frac{ dx }{ dt }\right)_{ t =4}\) is. 2022 Medium
68. 68. The velocity of the bullet becomes one third after it penetrates \(4\,cm\) in a wooden block. Assuming that bullet is facing a constant resistance during its motion in the block. The bullet stops completely after travelling at \((4+x)\,cm\) inside the block. The value of \(x\) is\(.....\) 2022 Medium
69. 69. 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 \(g =10 \,ms ^{-2}\) ] 2022 Hard
70. 70. Two cars \(P\) and \(Q\) start from a point at the same time in a straight line and their positions are represented by \( x_p(t)=at+bt^2 \) and \(x_Q(t)= ft- t^2\). At what time do the cars have the same velocity \(?\)  2022 Medium
71. 71. 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 ............ \(m\) 2022 Medium
72. 72. 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.(In \({m}\)) (Takes the value of \(g\) as \(10 \,{m} / {s}^{2}\) ) 2021 Hard
73. 73. A car accelerates from rest at a constant rate \(\alpha\) for some time after which it decelerates at a constant rate \(\beta\) to come to rest. If the total time elapsed is \(t\) seconds, the total distance travelled is 2021 Hard
74. 74. A particle is moving with constant acceleration \('a'.\) Following graph shows \(v^{2}\) versus \(x\) (displacement) plot. The acceleration of the particle is \(......{m} / {s}^{2}\)
    2021 Hard
75. 75. A particle is projected with velocity \(v_{0}\) along \(x-\) axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e., \(ma =-\alpha x ^{2}.\) The distance at which the particle stops: 2021 Hard
76. 76. 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 ..... . 2021 Hard
77. 77. 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 ..... \(m\). 2021 Hard
78. 78. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity \(u\) and the last compartment with velocity \(v\). The velocity with which middle point of the train passes the signal post is 2021 Medium
79. 79. If the velocity of a body related to displacement \({x}\) is given by \(v=\sqrt{5000+24 {x}} \;{m} / {s}\), then the acceleration of the body is \(\ldots \ldots {m} / {s}^{2}\) 2021 Hard
80. 80. Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time \(t_1\) . On other days, if she remains stationary on the moving escalator, then the escalator takes her up in time \(t_2\). The time taken by her to walk up on the moving escalator will be  2021 Medium
81. 81. The relation between time \(t\) and distance \(x\) for a moving body is given as \(t=m x^{2}+n x\), where \({m}\) and \({n}\) are constants. The retardation of the motion is - (Where \(v\) stands for velocity) 2021 Hard
82. 82. The velocity of a particle is \(v = v _{0}+ gt + Ft ^{2}\). Its position is \(x=0\) at \(t=0\); then its displacement after time \(( t =1)\) is : 2021 Easy
83. 83. Two spherical balls having equal masses with radius of \(5\, {cm}\) each are thrown upwards along the same vertical direction at an interval of \(3\, {s}\) with the same initial velocity of \(35 \,{m} / {s}\), then these balls collide at a height of \(\ldots \ldots \ldots . {m}\). (Take \({g}=10 \,{m} / {s}^{2}\) ) 2021 Hard
84. 84. Water droplets are coming from an open tap at 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 \(g=9.8\, {m} / {s}^{2}\)) 2021 Hard
85. 85. 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.  (In \(m\)) 2021 Hard
86. 86. A ball is dropped from the top of a \(100\; m\) high tower on a planet. In the last \(\frac{1}{2}\;s \) before hitting the ground, it covers a distance of \(19\; \mathrm{m}\). Acceleration due to gravity (in \(\mathrm{ms}^{-2}\) ) near the surface on that planet is 2020 Medium
87. 87. A helicopter reises 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] 2020 Hard
88. 88. The distance \(x\) covered by a particle in one dimensional motion varies with time \(t\) as \(\mathrm{x}^{2}=\mathrm{at}^{2}+2 \mathrm{bt}+\mathrm{c.}\) If the acceleration of the particle depends on \(\mathrm{x}\) as \(\mathrm{x}^{-\mathrm{n}},\) where \(\mathrm{n}\) is an integer, the value of \(\mathrm{n}\) is 2020 Hard
89. 89. The speed verses time graph for a particle is shown in the figure. The distance travelled (in \(m\) ) by the particle during the time interval \(t=0\) to \(t=5\, s\) will be
    2020 Easy
90. 90. The velocity \((v)\) and time \((t)\) graph of a body in a straight line motion is shown in the figure. The point \(S\) is at \(4.333\) seconds. The total distance covered by the body in \(6 \;s\) is\(.......m\)
    2020 Medium
91. 91. 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 \(1.8\, km / hr\). Speed (in \(ms ^{-1}\) ) of this person as observed from train \(B\) will be close to (take the distance between the tracks as negligible) 2020 Medium
92. 92. A particle is moving with speed \(v= b\sqrt x\) along positive \(x-\) axis. Calculate the speed of the particle at time \(t = \tau\) (assume that the particle is at origin at \(t = 0\) ). 2019 Hard
93. 93. A particle starts from origin \(O\) from rest and moves with a uniform acceleration along the positive \(x -\) axis. Identify all figures that correctly represent the motion qualitatively. (\(a =\) acceleration, \(v =\) velocity, \(x =\) displacement, \(t =\) time)
    2019 Hard
94. 94. A particle starts from the origin at time \(t = 0\) and moves along the positive \(x-\) axis. The graph of velocity with respect to time is shown in figure. What is the position of the particle at time \(t = 5\,s\) ?.........\(m\)
    2019 Easy
95. 95. A passenger train of length \(60\, m\) travels at a speed of \(80\, km/hr\). Another freight train of length \(120\, m\) travels at a speed of \(30\, km/hr\). The ratio of times taken by the passenger train to completely cross the freight train when: \((i)\) they are moving in the same direction, and \((ii)\) in the opposite directions is 2019 Hard
96. 96. In a car race on straight road, car \(A\) takes a time \(t\) less than car \(B\) at the finish and passes finishing point with a speed \(v\) more than that of car \(B.\) Both the cars start from rest and travel with constant acceleration \(a_1\) and \(a_2\) respectively. Then \(v\) is equal to 2019 Hard
97. 97. The position of a particle as a function of time \(t\), is given by \(x\left( t \right) = at+ b{t^2} - c{t^3}\) where \(a, b\) and \(c\) are constants. When the particle attains zero acceleration, then its velocity will be 2019 Hard
98. 98. A man in a car at location \(Q\) on a straight highway is moving with speed \(v\). He decides to reach a point \(P\) in a field at a distance \(d\) from highway (point \(M\) ) as shown in the figure.Speed of the car in the field is half to that on the highway. What should be the distance \(RM\), so that the time taken to reach \(P\) is minimum?
    2018 Hard
99. 99. An automobile, travelling at \(40\, km/h\), can be stopped at a distance of \(40\, m\) by applying brakes. If the same automobile is travelling at \(80\, km/h\), the minimum stopping distance, in metres, is (assume no skidding)..........\(m\) 2018 Medium
100. 100. The velocity-time graphs of a car and a scooter are shown in the figure. \((i)\) the difference between the distance travelled by the car and the scooter in \(15\, s\) and \((ii)\) the time at which the car will catch up with the scooter are, respectively
     2018 Hard

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