JEE Physics - Motion in a Straight Line

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Question - 1

A body of mass m is thrown straight up with velocity v0. Find the velocity v' wirh which the body comes down if the air drag equals kv2,where t is a constant and v is the velocity of the body.

  • A \(v^{\prime}=\frac{v_{0}}{\sqrt{1+\frac{k v_{0}^{2}}{m g}}} \)
  • B \( v^{\prime}=\frac{v_{0}}{\sqrt{1-\frac{k v_{0}^{2}}{m g}}}\)
  • C \(v^{\prime}=\frac{v_{0}}{\sqrt{1+\frac{k v_{0}}{m g}}}\)
  • D \(v^{\prime}=\frac{v_{0}}{\sqrt{1-\frac{k v_{0}}{m g}}}\)

Question - 2

From point A located on a highway as shown in figure. one has to get by car as soon as possible to point B located in the field ar a distane / from the highway. It is knorm that car moves in the field \(\eta\) time slower on the highway. At what disare from point D one must turn off the highway?

  • A \(x=\frac{\ell}{\sqrt{\eta^{2}+1}} \)
  • B \(x=\frac{\ell}{\sqrt{\eta^{2}-1}} \)
  • C \(x=\frac{\ell}{\sqrt{\eta^{4}+1}} \)
  • D \(x=\frac{\ell}{\sqrt{\eta^{4}-1}} \)

Question - 3

Having gone through a plank of thickness h, a bullet changed its velocity from v0 to v. Find the time of motion of the bullet in the plank, assuming the resistance force to be proportional to the square of the velocity.

  • A \(t=\left[\begin{array}{l}\frac{h\left(v_{0}+v\right)}{v v_{0} \ell \mathrm{n} \frac{v_{0}}{v}}\end{array}\right]\)
  • B \(t=\left[\frac{h\left(v_{0}-v\right)}{v v_{0} \ell \ln \frac{v}{v_{0}}}\right]\)
  • C \(t=\left[\frac{h\left(v_{0}-v\right)}{v v_{0} \ell \mathrm{n} \frac{v_{0}}{v}}\right]\)
  • D \(t=\left[\frac{h\left(v_{0}+v\right)}{v v_{0} \ell \mathrm{n} \frac{v_{0}}{v}}\right]\)

Question - 4

A stone is dropped from a height h, simultaneously another stone is thrown up from the ground which at a height 4h, the two stones cross each other after time_____

  • A \(\sqrt{\frac{h}{2 g}}\)
  • B \(\sqrt{\frac{h}{8 g}}\)
  • C \(\sqrt{8 h g}\)
  • D \(\sqrt{2 h g}\)

Question - 5

A drunkard walking in a narrow lane takes 5 steps forward and 3 steps backward, followed again by.5 steps forward and 3 steps backward, and so on. Each step is I m long and requires 1 s. The time when he will fall into the pit 13 m away from him is ___

  • A 13 s
  • B 37 s
  • C 40 s
  • D 42 s

Question - 6

Starting from rest a particle moves in a straight line with acceleration a = {2 + |t - 2|} m/s2. Velocity of particle at the end of 4 s will be_____

  • A 16 m/s
  • B 20 m/s
  • C 8 m/s
  • D 12 m/s

Question - 7

A car of mass m is travelling at a slow velocity v0. It is subjected to a drag resistance of the wind, which is proportional to its velocity, the constant of proportionality being k. The distance covered by the car before its speed becomes half is______

  • A \(\frac{m v_{0}}{k}\)
  • B \(\frac{2 m v_{0}}{k}\)
  • C \(\frac{m v_{0}}{2 k}\)
  • D \(\frac{m v_{0}}{4 k}\)

Question - 8

A ball is thrown horizontally from a height with a certain velocity at time t = 0. The ball bounces repeatedly from the ground with coefficient of restitution less than I as shown. Neglecting air resistance and taking the upward direction as positive, which figure qualitatively depits the vertical component of the balls velocity (vy) as a function of time (t) ____

  • A
  • B
  • C
  • D

Question - 9

The velocity-displacement graph of a particle moving along a straight line is shown in figure. Then the acceleration-displacement graph is_____

  • A
  • B
  • C
  • D

Question - 10

Particles A and B are moving as shown in the diagram. What is their velocity of separation.

  • A 4.8 m/s
  • B 3.8 m/s
  • C 2.8 m/s
  • D 1.8 m/s
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