JEE Main & Advanced Physics Motion in a Straight Line / सरल रेखा में गति Sample Paper

done Topic Test - One Dimensional Motion Total Questions - 35    [Download]

• question_answer1)
  If the velocity \[\upsilon \] of a particle moving along a straight line decreases linearly with its displacement S is \[20\,\,m{{s}^{-1}}\] to a value approaching to zero at \[S=30\,m,\] then acceleration of the particle at \[S=15\text{ }m,\] is
  A)
  \[\frac{2}{3}m{{s}^{-2}}\]
  done clear
  B)
  \[-\frac{2}{3}m{{s}^{-2}}\]
  done clear
  C)
  \[\frac{20}{3}m{{s}^{-2}}\]
  done clear
  D)
  \[-\frac{20}{3}m{{s}^{-2}}\]
  done clear
  View Answer play_arrow

• question_answer2)
  A body is thrown vertically upward in air when air resistance is taken into account, the time of ascent is \[{{t}_{1}}\] and time of descent is \[{{t}_{2}}\], then which of the following is true?
  A)
  \[{{t}_{1}}={{t}_{2}}\]
  done clear
  B)
  \[{{t}_{1}}<{{t}_{2}}\]
  done clear
  C)
  \[{{t}_{1}}>{{t}_{2}}\]
  done clear
  D)
  \[{{t}_{1}}\ge \,\,{{t}_{2}}\]
  done clear
  View Answer play_arrow

• question_answer3)
  A point moves with uniform acceleration and \[{{v}_{1}},\text{ }{{v}_{2}},\text{ }{{v}_{3}}\] denote the average velocities in three successive intervals of time \[{{t}_{1}},\text{ }{{t}_{2}},\text{ }{{t}_{3}}\]. Which of the following relations is correct?
  A)
  \[({{v}_{1}}{{v}_{2}}):({{v}_{2}}{{v}_{3}})=({{t}_{1}}{{t}_{2}}):\text{(}{{t}_{2}}+{{t}_{3}})\]
  done clear
  B)
  \[({{v}_{1}}{{v}_{2}}):({{v}_{2}}{{v}_{3}})=({{t}_{1}}+{{t}_{2}}):\text{(}{{t}_{2}}+{{t}_{3}})\]
  done clear
  C)
  \[({{v}_{1}}{{v}_{2}}):({{v}_{2}}{{v}_{2}})=({{t}_{1}}-{{t}_{2}}):\text{(}{{t}_{2}}-{{t}_{3}})\]
  done clear
  D)
  \[({{v}_{1}}{{v}_{2}}):({{v}_{2}}+{{v}_{3}})=({{t}_{1}}-{{t}_{2}}):\text{(}{{t}_{2}}+{{t}_{3}})\]
  done clear
  View Answer play_arrow

• question_answer4)
  A boy sitting on the top most berth in the compartment of a train which is just going to stop on a railway station, drops an apple aiming at the open hand of his brother situated vertically below his hands at a distance of about 2 m. The apple will fall
  A)
  precisely in the hand of his brother
  done clear
  B)
  slightly away from the hand of his brother in the direction of motion of the train
  done clear
  C)
  slightly away from the hand of his brother in the direction opposite to the direction of motion of the train
  done clear
  D)
  None of the above
  done clear
  View Answer play_arrow

• question_answer5)
  The velocity-time graph of a body is shown in figure. It implies that at point B.
  A)
  the force is zero
  done clear
  B)
  there is a force towards motion
  done clear
  C)
  there is a force which opposes motion
  done clear
  D)
  there is only gravitational force
  done clear
  View Answer play_arrow

• question_answer6)
  A juggler throws balls into air. He throws one whenever previous one is at its highest point, if he throws n balls per second, then the height to which each ball will rise is
  A)
  \[g/n\]
  done clear
  B)
  \[g/{{n}^{2}}\]
  done clear
  C)
  \[g/2{{n}^{2}}\]
  done clear
  D)
  \[g/4{{n}^{2}}\]
  done clear
  View Answer play_arrow

• question_answer7)
  The displacement \[\times \] of a particle is given by \[x=a{{e}^{-\alpha t}}+b{{e}^{\beta t}}\] with \[a,\,b,\,\alpha \] and \[\beta \] as constants. With increase in time, the associated velocity
  A)
  increases                     
  done clear
  B)
  decreases
  done clear
  C)
  increases and decreases
  done clear
  D)
  decreases and increases
  done clear
  View Answer play_arrow

• question_answer8)
  A wooden block is dropped from the top of a cliff 100 m high. Simultaneously a bullet is fired from the foot of the cliff upward with a velocity of 100 m/s. The bullet hits the wooden block after - \[[Takeg=10\text{ }m/{{s}^{2}}]\]
  A)
  10 s
  done clear
  B)
  0.5 s
  done clear
  C)
  1 s
  done clear
  D)
  7 s
  done clear
  View Answer play_arrow

• question_answer9)
  A bus is beginning to move with an acceleration of \[1\text{ }m{{s}^{2}}\]. A boy who is 48 m behind the bus starts running at \[10\text{ }m{{s}^{1}}\]. After what time will the boy be able to catch the bus?
  A)
  6 s
  done clear
  B)
  8 s
  done clear
  C)
  10 s     
  done clear
  D)
  The boy cannot catch the bus
  done clear
  View Answer play_arrow

• question_answer10)
  A train is moving along a straight path with uniform acceleration. Its engine passes across a pole with a velocity of \[60\text{ }km{{h}^{1}}\] and the end (guard's van) passes across same pole with a velocity of \[60\text{ }km{{h}^{1}}\]. The middle point of the train will pass across same pole with a velocity
  A)
  \[70\text{ }km{{h}^{1}}\]
  done clear
  B)
  \[70.7\text{ }km{{h}^{1}}\]
  done clear
  C)
  \[65\text{ }km{{h}^{1}}\]
  done clear
  D)
  \[75\text{ }km{{h}^{1}}\]
  done clear
  View Answer play_arrow

• question_answer11)
  A point moves in a straight line so that its displacement x metre at time t second is given by \[{{x}^{2}}=1+{{t}^{2}}\]. Its acceleration in \[m{{s}^{2}}\] at time second is
  A)
  \[\frac{1}{{{x}^{3}}}\]
  done clear
  B)
  \[\frac{1}{x}\,-\frac{1}{{{x}^{2}}}\]
  done clear
  C)
  \[-\frac{t}{{{x}^{2}}}\]
  done clear
  D)
  \[\frac{1}{x}\,-\,\frac{{{t}^{2}}}{{{x}^{3}}}\]
  done clear
  View Answer play_arrow

• question_answer12)
  A body starts with some initial velocity and a constant acceleration. It covers a distance of 200 m in first four second and a distance of 220 m in next two second. The acceleration of the body and its velocity at the end of seventh second are
  A)
  \[a=5\,m{{s}^{-2}},\,\,\upsilon =75\,m{{s}^{-1}}\]
  done clear
  B)
  \[a=7.5\,m{{s}^{-2}},\,\upsilon =100\,m{{s}^{-1}}\]
  done clear
  C)
  \[a=20\,m{{s}^{-2}},\,\upsilon =150\,m{{s}^{-1}}\]
  done clear
  D)
  \[a=150\,m{{s}^{-2}},\,\upsilon =10\,m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer13)
  If a car covers 2/5th of the total distance with \[{{v}_{1}}\] speed and 3/5th distance with \[{{v}_{2}},\] then average speed is
  A)
  \[\frac{1}{2}\,\sqrt{{{v}_{1}}{{v}_{2}}}\]
  done clear
  B)
  \[\frac{{{v}_{1}}+{{v}_{2}}}{2}\]
  done clear
  C)
  \[\frac{2{{v}_{1}}{{v}_{2}}}{{{v}_{1}}+{{v}_{2}}}\]
  done clear
  D)
  \[\frac{5{{v}_{1}}{{v}_{2}}}{3{{v}_{1}}+2{{v}_{2}}}\]
  done clear
  View Answer play_arrow

• question_answer14)
  A stone dropped from a building of height h and it reaches after t seconds on earth. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u and they reach the earth surface after \[{{t}_{1}}\] and \[{{t}_{2}}\] seconds, respectively, then
  A)
  \[t={{t}_{1}}-{{t}_{2}}\]
  done clear
  B)
  \[t=\frac{{{t}_{1}}+{{t}_{2}}}{2}\]
  done clear
  C)
  \[t=\sqrt{{{t}_{1}}{{t}_{2}}}\]
  done clear
  D)
  \[t_{1}^{2}=t_{2}^{2}\]
  done clear
  View Answer play_arrow

• question_answer15)
  A body starts from rest with uniform acceleration. If its velocity after n second is l), then its displacement in the last two seconds is
  A)
  \[\frac{2\upsilon (n+1)}{n}\]
  done clear
  B)
  \[\frac{\upsilon (n+1)}{n}\]
  done clear
  C)
  \[\frac{\upsilon (n-1)}{n}\]
  done clear
  D)
  \[\frac{2\upsilon (n-1)}{n}\]
  done clear
  View Answer play_arrow

• question_answer16)
  A particle is moving rectilinearly with acceleration a, whose value is given as a function of distance by the equation \[a=\alpha \sqrt{x},\] find displacement as a function of time. [At \[t=0,\] particle is at rest at \[x=0\]]
  A)
  \[\frac{4a{{t}^{3}}}{2}\]
  done clear
  B)
  \[\left( \frac{\sqrt{\alpha }}{6} \right)t\]
  done clear
  C)
  \[\left( \frac{{{\alpha }^{2}}}{36} \right){{t}^{4}}\]
  done clear
  D)
  \[\left( \frac{{{\alpha }^{2}}}{144} \right){{t}^{4}}\]
  done clear
  View Answer play_arrow

• question_answer17)

  Direction: A particle initially (i.e., at time \[t=0\]) moving with a velocity u subjected to a retarding force, as a result of which it decelerates at a rate \[a=-k\,\sqrt{v}\] where v is the instantaneous velocity and k is a positive constant.

  The particle comes to rest in a time

  A)
  \[\frac{2\sqrt{u}}{k}\]
  done clear
  B)
  \[\frac{\sqrt{u}}{k}\]
  done clear
  C)
  \[2k\sqrt{u}\]
  done clear
  D)
  \[k\sqrt{u}\]
  done clear
  View Answer play_arrow

• question_answer18)

  Direction: A particle initially (i.e., at time \[t=0\]) moving with a velocity u subjected to a retarding force, as a result of which it decelerates at a rate \[a=-k\,\sqrt{v}\] where v is the instantaneous velocity and k is a positive constant.

  The distance covered by the particle before coming to rest is

  A)
  \[\frac{{{u}^{3/2}}}{k}\]
  done clear
  B)
  \[\frac{2{{u}^{3/2}}}{k}\]
  done clear
  C)
  \[\frac{3{{u}^{3/2}}}{2k}\]
  done clear
  D)
  \[\frac{2{{u}^{3/2}}}{3k}\]
  done clear
  View Answer play_arrow

• question_answer19)
  A body covered a distance of L m along a curved path of a quarter circle. The ratio of distance to displacements
  A)
  \[\frac{\pi }{2\sqrt{2}}\]
  done clear
  B)
  \[\frac{2\sqrt{2}}{\pi }\]
  done clear
  C)
  \[\frac{\pi }{\sqrt{2}}\]          
  done clear
  D)
  \[\frac{\sqrt{2}}{\pi }\]
  done clear
  View Answer play_arrow

• question_answer20)
  A particle is resting over a smooth horizontal floor. At \[t=0\] a horizontal force starts acting on it. Magnitude of the force increases with time according to law \[G=\alpha t,\] where a is a positive constant and t is time. For the figure shown which of the following statements is/are incorrect?
  A)
  Curve 1 shows acceleration against time
  done clear
  B)
  Curve 2 shows velocity against time
  done clear
  C)
  Curve 2 shows velocity against acceleration
  done clear
  D)
  none of these
  done clear
  View Answer play_arrow

• question_answer21)
  The velocity v and position r of a body are related as, \[{{v}^{2}}=kr,\] where k is a constant. What will be the velocity after 1 second? Given that the position is zero at \[t=0\].
  A)
  \[\sqrt{kr}\]
  done clear
  B)
  \[k{{r}^{-3/2}}\]
  done clear
  C)
  \[\frac{k}{2}{{r}^{0}}\]                 
  done clear
  D)
  cannot be determined from the given information
  done clear
  View Answer play_arrow

• question_answer22)
  Two balls of equal masses are thrown upwards, along the same vertical direction at an interval of 2 seconds, with the same initial velocity of 40 m/s. Then these collide at a height of (Take \[g=10\,m/{{s}^{2}}\])
  A)
  120 m
  done clear
  B)
  75 m
  done clear
  C)
  200 m
  done clear
  D)
  45 m
  done clear
  View Answer play_arrow

• question_answer23)
  A person climbs up a stalled escalator in 60 sec. When he stands on it then he is carried in the moving escalator in 30 sec. How much time will he take in climbing up in a moving escalator?
  A)
  10 sec
  done clear
  B)
  30 sec 
  done clear
  C)
  20 sec
  done clear
  D)
  40 sec
  done clear
  View Answer play_arrow

• question_answer24)
  The position of a particle vary \[x=4t-2{{t}^{2}}\]. The distance covered by particle in 4 s is
  A)
  5 m
  done clear
  B)
  1 m
  done clear
  C)
  2 m
  done clear
  D)
  4 m
  done clear
  View Answer play_arrow

• question_answer25)
  A body moves in a straight line along x-axis. Its distance from the origin is given by\[x=9t-3{{t}^{2}}\]. The average velocity between \[t=0\] to \[t=4\] is
  A)
  \[-3\,m{{s}^{-1}}\]
  done clear
  B)
  \[4\,m{{s}^{-1}}\]
  done clear
  C)
  \[-16\,m{{s}^{-1}}\]
  done clear
  D)
  \[-12\,m{{s}^{-1}}\]
  done clear
  View Answer play_arrow

• question_answer26)
  Balls are dropped from the roof of a tower at a fixed interval of time. At the time when 9th ball reaches the ground, nth ball is at 3/4th height of the tower. The value of n is
  A)
  3
  done clear
  B)
  7
  done clear
  C)
  6
  done clear
  D)
  5
  done clear
  View Answer play_arrow

• question_answer27)
  A rifle bullet loses \[\frac{1}{4}\] of its velocity in passing through a wooden plank. The least number of planks required to stop the bullet is (assume uniform retardation in the plank)
  A)
  4
  done clear
  B)
  5
  done clear
  C)
  2
  done clear
  D)
  3
  done clear
  View Answer play_arrow

• question_answer28)
  A body starts from rest with uniform acceleration a, its velocity after n seconds is \[\upsilon \]. The displacement of the body in last 3 seconds is:
  A)
  \[\frac{\upsilon (6n-9)}{2n}\]
  done clear
  B)
  \[\frac{2\upsilon (6n-9)}{n}\]
  done clear
  C)
  \[\frac{2\upsilon (2n+1)}{n}\]
  done clear
  D)
  \[\frac{2\upsilon (n-1)}{n}\]
  done clear
  View Answer play_arrow

• question_answer29)
  Two buses moving in opposite directions with velocities of 16 m/s and 12 m/s have lengths of 6 m and 8 m respectively. The minimum road length required for overtaking is
  A)
  14 m
  done clear
  B)
  28 m
  done clear
  C)
  22 m
  done clear
  D)
  20 m
  done clear
  View Answer play_arrow

• question_answer30)
  A force F acts on a body of mass 1 kg moving in a straight line with an initial velocity u for 1s, then
  A)
  distance covered by the body is \[u+F/2\]
  done clear
  B)
  momentum of the body increases by F
  done clear
  C)
  final velocity of the body is \[u\text{ }+\text{ }F\]
  done clear
  D)
  all of these
  done clear
  View Answer play_arrow

• question_answer31)
  The engine of a motor cycle can produce maximum acceleration \[5\text{ }m/se{{c}^{2}}\]. Its breaks can produce a maximum retardation \[10\text{ }m/se{{c}^{2}}\]. What is minimum time in which it can cover a distance of 1.5 km:
  A)
  5 sec.
  done clear
  B)
  10 sec.           
  done clear
  C)
  15 sec.
  done clear
  D)
  30 sec.
  done clear
  View Answer play_arrow

• question_answer32)
  A body moves with uniformly accelerated motion and travels 200 cm in the first two seconds and 220 cm in the next four seconds. What will be the velocity at the end of 7 seconds from start?
  A)
  - 10 cm/s
  done clear
  B)
  10 cm/s
  done clear
  C)
  20 cm/s
  done clear
  D)
  30 cm/s
  done clear
  View Answer play_arrow

• question_answer33)
  A point mass starts moving in straight line with constant acceleration a from rest at \[t=0.\] At time \[t=2s\], the acceleration changes the sign, remaining the same in magnitude. The mass returns to the initial position at time \[t={{t}_{0}}\] after start of motion. Here \[{{t}_{0}}\] is:
  A)
  4s
  done clear
  B)
  \[(4+2\sqrt{2})s\]
  done clear
  C)
  \[(2+2\sqrt{2})s\]
  done clear
  D)
  \[(4+4\sqrt{2})s\]
  done clear
  View Answer play_arrow

• question_answer34)
  A cyclist starts from the centre O of a circular track of radius R = 2 km, moves along radius OP and then moves from P to Q along the circumference and there at Q it stops. The total time of motion of the cyclist is 45 min. The average speed of the cyclist is
  A)
  8 km/h
  done clear
  B)
  6.86 km/h
  done clear
  C)
  15.23 km/h
  done clear
  D)
  None of these
  done clear
  View Answer play_arrow

• question_answer35)
  Acceleration versus velocity graph of a particle moving in a straight line is as shown in figure. The corresponding velocity-time graph would be
  A)
  
  done clear
  B)
  
  done clear
  C)
  
  done clear
  D)
  
  done clear
  View Answer play_arrow