# Solved papers for JEE Main & Advanced Physics Motion in a Straight Line / सरल रेखा में गति JEE PYQ - One Dimensional Motion

### done JEE PYQ - One Dimensional Motion Total Questions - 37

• question_answer1) From a building, two balls A and B are thrown such that A is thrown upwards and B downwards (both vertically). If ${{v}_{A}}$ and ${{v}_{B}}$ are their respective velocities on reaching the ground, then                        [AIEEE 2002]

A)
${{v}_{B}}>{{v}_{A}}$

B)
${{v}_{A}}={{v}_{B}}$

C)
${{v}_{A}}>{{v}_{B}}$

D)
their velocities depend on their masses

• question_answer2) If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest?                                                   [AIEEE 2002]

A)
1 cm

B)
2cm

C)
3 cm

D)
4 cm

• question_answer3) A car moving with a speed of 50 km/h, can be stopped by brakes after atleast 6 m. If the same car is moving at a speed of 100 km/h, the minimum stopping distance is    [AIEEE 2003]

A)
12m

B)
18m

C)
24m

D)
6m

• question_answer4) A particle moves in a straight line with retardation proportional to its displacement. Its loss of kinetic energy for any displacement x is proportional to                                 [AIEEE 2004]

A)
${{x}^{2}}$

B)
${{e}^{x}}$

C)
$x$

D)
${{\log }_{e}}x$

• question_answer5) A ball is released from the top of a tower of height h metre. It takes T second to reach the ground. What is the position of the ball in$T/3s$                                              [AIEEE 2004]

A)
$h/9$m from the ground

B)
$7h/9$m from the ground

C)
$8h/9$m from the ground

D)
$17h/18$m from the ground

• question_answer6) An automobile travelling with a speed of 60 km/h, can brake to stop within a distance of 20 m. If the car is going twice as fast, i.e., 120 km/h, the stopping distance will be       [AIEEE 2004]

A)
20 m

B)
40 m

C)
60 m

D)
80 m

• question_answer7) A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?                            [AIEEE 2005]

A)
3.0 cm

B)
2.0 cm

C)
1.5 cm

D)
1.0 cm

• question_answer8) The relation between time t and distance$x$is $t=a{{x}^{2}}+bx,$where a and b are constants. The acceleration is                         [AIEEE 2005]

A)
$-2ab{{v}^{2}}$

B)
$2b{{v}^{3}}$

C)
$-2a{{v}^{3}}$

D)
$2a{{v}^{2}}$

• question_answer9) A car, starting from rest, accelerates at the rate f through a distance S, then continues at constant speed for time t and then decelerates at the rate f/2 to come to rest. If the total distance travelled is 15 S, then [AIEEE 2005]

A)
$S=ft$

B)
$S=\frac{1}{6}f{{t}^{2}}$

C)
$S=\frac{1}{2}f{{t}^{2}}$

D)
None of these

• question_answer10) A parachutist after bailing out falls 50 m without friction. When parachute opens, it decelerates at$2m/{{s}^{2}}$. He peaches the ground with a speed of 3 m/s. At what height, did he bail out? [AIEEE 2005]

A)
91 m

B)
182m

C)
293m

D)
111 m

• question_answer11) A particle located at$x=0$at time$t=0$, starts moving along the positive x-direction with a velocity v that varies as$v=\alpha \sqrt{x}$. The displacement of the particle varies with time as                                             [AIEEE 2006]

A)
${{t}^{2}}$

B)
$t$

C)
${{t}^{1/2}}$

D)
${{t}^{3}}$

• question_answer12) The   velocity   of   a   particle   is$x$If its position is$x$at$\frac{{{x}^{2}}}{{{\cos }^{2}}\alpha }-\frac{{{y}^{2}}}{{{\sin }^{2}}\alpha }=1,$then its displacement after unit time$\frac{\pi }{4}$is                                               [AIEEE 2007]

A)
$\pi /6$

B)
$\pi /3$

C)
$\pi /4$

D)
$\pi /2$

• question_answer13) A body is at rest at $x=0$. At $t=0$, it starts moving in the positive x-direction with a constant acceleration. At the same instant another body passes through $x=0$ moving in the positive x direction with a constant speed. The position of the first body is given by ${{x}_{1}}(t)$after time t and that of the second body by ${{x}_{2}}(t)$ after the same time interval. Which of the following graphs correctly describes $({{x}_{1}}-{{x}_{2}})$ as a function of time t?           [AIEEE 2008]

A)

B)

C)

D)

• question_answer14)  Consider a rubber ball freely falling from a height$h=4.9\text{ }m$onto a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Then the velocity as a function of time and the height as a function of time will be:     [AIEEE 2009]

A)

B)

C)

D)

• question_answer15) An object, moving with a speed of $6.25\,m/s$, is decelerated at a rate given by $\frac{d\upsilon }{dt}=-2.5\sqrt{v}$ where v is the instantaneous speed. The time taken by the object, to come to rest, would be [AIEEE 2011]

A)
8 s

B)
1 s

C)
2 s

D)
4 s

• question_answer16)  The graph of an object's motion (along the x- axis) is shown in the figure. The instantaneous velocity of the object at points A and B are ${{v}_{A}}$ and ${{v}_{B}}$ respectively. Then        [JEE ONLINE 07-05-2012]

A)
${{v}_{A}}={{v}_{B}}=0.5m/s$

B)
${{v}_{A}}=0.5m/s<{{v}_{B}}$

C)
${{v}_{A}}=0.5m/s>{{v}_{B}}$

D)
${{v}_{A}}={{v}_{B}}=2m/s$

• question_answer17)  The distance travelled by a body moving along a line in time / is proportional to t3. The acceleration-time (a, t) graph for the motion of the body will be  [JEE ONLINE 12-05-2012]

A)

B)

C)

D)

• question_answer18) A goods train accelerating uniformly on a straight railway track, approaches an electric pole standing on the side of track. Its engine passes the pole with velocity u and the guard's room passes with velocity v. The middle wagon of the train passes the pole with a velocity. [JEE ONLINE 19-05-2012]

A)
$\frac{u+v}{2}$

B)
$\frac{1}{2}\sqrt{{{u}^{2}}+{{v}^{2}}}$

C)
$\sqrt{uv}$

D)
$\sqrt{\left( \frac{{{u}^{2}}+{{v}^{2}}}{2} \right)}$

• question_answer19)  From a tower of height H, a particle is thrown vertically upwards with a speed U. The time taken by the particle, to hit the ground, is n times that taken by it to reach the highest point of its path.            [JEE MAIN 2014] The relation between H, u and n is:

A)
$2gH=n{{u}^{2}}(n-2)$

B)
$gH=(n-2){{u}^{2}}$

C)
$2gH={{n}^{2}}{{u}^{2}}$

D)
$gH={{(n-2)}^{2}}{{u}^{2}}$

• question_answer20) A bullet looses ${{\left( \frac{1}{n} \right)}^{th}}$of its velocity passing through one plank. The number of such planks that are required to stop the bullet can be:                        [JEE ONLINE 19-04-2014]

A)
$\frac{{{n}^{2}}}{2n-1}$

B)
$\frac{2{{n}^{2}}}{n-1}$

C)
infinite

D)
n

• question_answer21)  Two stones are thrown up simultaneously from the edge of a cliff 240 m high with initial speed of m/s and 40 m/s respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect of the first? (Assume stones do not rebound after hitting the ground and neglect air resistance, take g = 10 m/s2) (The figure are schematic and not drawn to scale)                                 [JEE MAIN 2015]

A)

B)

C)

D)

• question_answer22) Which graph corresponds to an object moving with a constant negative acceleration and a positive velocity?    [JEE Online 08-04-2017]

A)

B)

C)

D)

• question_answer23) A car is standing 200 m behind a bus, which is also at rest. The two start moving at the same instant but with different forward accelerations. The bus has acceleration $2\,m/{{s}^{2}}$ and the car has acceleration $4\,m/{{s}^{2}}$. The car will catch up with the bus after at time of -   [JEE Online 09-04-2017]

A)
$\sqrt{120}\,s$

B)
$15\,s$

C)
$\sqrt{110}\,s$

D)
$10\sqrt{2}\,s$

• question_answer24) All the graphs below are intended to represent the same motion. One of them does it incorrectly. Pick it up. [JEE Main Online 08-04-2018]

A)

B)

C)

D)

• question_answer25)  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 15s and (ii) the time at which the car will catch up with the scooter are, respectively [JEE Online 15-04-2018]

A)
$337.5m\,\,\,and\,\,25s$

B)
$225.5m\,\,and\,\,10s$

C)
$112.5m\,\,and\,\,22.5s$

D)
$11.2.5m\,\,and\,\,15s$

• question_answer26)  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? [JEE Online 15-04-2018 (II)]

A)
$\frac{d}{\sqrt{3}}$

B)
$\frac{d}{2}$

C)
$\frac{d}{\sqrt{2}}$

D)
$d$

• question_answer27) 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 ${{a}_{1}}\text{ }and\text{ }{{a}_{2}}$ respectively. Then v is equal to: [JEE Main 09-Jan-2019 Evening]

A)
$\sqrt{{{a}_{1}}\,{{a}_{2}}}\,\,t$

B)
$\frac{2{{a}_{1}}{{a}_{2}}}{{{a}_{1}}+{{a}_{2}}}\,\,t$

C)
$\frac{{{a}_{1}}+{{a}_{2}}}{2}\,\,t$

D)
$\sqrt{2{{a}_{1}}{{a}_{2}}}\,\,t$

• question_answer28) A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity $100\text{ }m{{s}^{-1}}$from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is - $(g=10\,m{{s}^{-2}})$ [JEE Main 10-Jan-2019 Morning]

A)
30 m

B)
40 m

C)
20 m

D)
10 m

• question_answer29)  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   $t=5s$? [JEE Main 10-Jan-2019 Evening]

A)
3 m

B)
9 m

C)
10 m

D)
6 m

• question_answer30)  A particle moves in one dimension from rest under the influence of a force that varies with the distance travelled by the particle as shown in the figure. The kinetic energy of the particle after it has travelled 3m is: [JEE Main 8-4-2019 Morning]

A)
6.5 J

B)
2.5 J

C)
4 J

D)
5 J

• question_answer31)  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. [JEE Main 8-4-2019 Afternoon] (a = acceleration, v = velocity, x = displacement, t = time)

A)
, ,

B)

C)
, ,

D)
,

• question_answer32)  The position of a particle as a function of time t, is given by $x(t)=at\,+b{{t}^{2}}-c{{t}^{3}}$ where a, b and c are constants. When the particle attains zero acceleration, then its velocity will be: [JEE Main 9-4-2019 Afternoon]

A)
$a+\frac{{{b}^{2}}}{4c}$

B)
$a+\frac{{{b}^{2}}}{c}$

C)
$a+\frac{{{b}^{2}}}{2c}$

D)
$a+\frac{{{b}^{2}}}{3c}$

• question_answer33) The position vector of a particle changes with time according to the relation $\vec{r}(t)=15{{t}^{2}}\hat{i}+(4-{{20}^{2}})\hat{j}.$ What is the magnitude of the acceleration at t = 1? [JEE Main 9-4-2019 Afternoon]

A)
40

B)
100

C)
25

D)
50

• question_answer34) A shell is fired from a fixed artillery gun with an initial speed u such that it hits the target on the ground at a distance R from it. If ${{t}_{1}}$ and ${{t}_{2}}$are the values of the time taken by it to hit the target in two possible ways, the product ${{t}_{1}}{{t}_{2}}$is: [JEE Main Held on 12-4-2019 Morning]

A)
$R/g$

B)
$R/4g$

C)
$2R/g$

D)
$R/2g$

• question_answer35) A particle is moving with speed $\text{v}\,\text{=}\,\text{b}\sqrt{x}$ along positive x-axis. Calculate the speed of the particle at time $t=\tau$(assume that the particle is at origin at t = 0). [JEE Main 12-4-2019 Afternoon]

A)
$\frac{{{b}^{2}}\tau }{4}$

B)
$\frac{{{b}^{2}}\tau }{2}$

C)
${{b}^{2}}\tau$

D)
$\frac{{{b}^{2}}\tau }{\sqrt{2}}$

• question_answer36) A ball is dropped from the to 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 m. Acceleration due to gravity (in $m{{s}^{-2}}$) near the surface on that planet is _______.  [JEE MAIN Held on 08-01-2020 Evening]

• question_answer37) The distance x covered by a particle in one dimensional motion varies with time t as ${{x}^{2}}\text{ }=\text{ }a{{t}^{2}}\text{ }+\text{ }2bt\text{ }+\text{ }c$. If the acceleration of the particle depends on x as${{x}^{n}}$, where n is an integer, the value of n is _____. [JEE MAIN Held on 09-01-2020 Morning]