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DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics PDF Download

Match the Columns

Ques 1: Match the following two columns.

Column I
Column II
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics(p) speed must be increasing
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics(q) speed must be decreasing
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics(r) speed may be increasing
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics(s) speed may be decreasing

Ans: (a) → r,s (b) →  r,s (c) →  p (d) →  q
Sol: 
(a)

DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
∴ v must be increasing with time.
⇒ speed must also be increasing with time.
(c) → (p).
(d) Slope is + ive and decreasing.
∴ Velocity must be decreasing with time.
⇒ speed must also be decreasing with time. (d) → (q).

Ques 2: Match the following two columns.

Column I
Column II
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics(p) speed increasing
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics(q) speed decreasing
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics(r) speed constant
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics(s) Nothing can be said

Ans: (a) → P (b) → p (c) → q (d) → q
Sol:
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics 
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
Speed increasing.
∴ (a) → (p).
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
As t > 0,  DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
or DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
At t = 0 s  DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics

DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics

Ques 3: The velocity-time graph of a particle moving along X-axis is shown in figure. Match the entries of Column I with entries of Column II.
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics

Column I
Column II
(a) For AB, particle is
(p) Moving in +ve X-direction with increasing speed
(b) For BC, particle is
(q) Moving in +ve X-direction with decreasing speed
(c) For CD, particle is
(r) Moving in -ve X-direction with increasing speed
(d) For ZXE, particle is
(s) Moving in +ve X-direction with decreasing speed

Ans: (a) → P (b) → p (c) → q (d) → r
Sol: (a) From A to B, v is increasing and area is + ive.
∴ (a) → (p).
(b) From B to C, v is increasing and area is + ive.
∴ (b) → (p).
(c) From C to D, v is decreasing while area is + ive.
∴ (c) → (q).
(d) From D to E, v is - ive and DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physicsis
increasing, area is -ive.
∴ (d) → (r).

Ques 4: Corresponding to velocity-time graph in one dimensional motion of a particle is shown in figure, match the following two columns.
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics

Column I
Column II
(a) Average velocity between zero sec and 4 s
(p) 10 SI units
(b) Average acceleration between 1 s and 4 s
(q) 2.5 SI units
(c) Average speed between zero
(r) 5 SI units
(d) Rate of change of speed at 4s
(s) None

Ans: (a) → (r) (b) → (s) (c) → (r) (d) → (r)
Sol: (a) Displacement = Area DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
i.e., (a) → (r).
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
= 5.83 unit
∴(b) → (s)
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
∴ (c) → (s)
(d) Rate of change of velocity at t = 4 s
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
∴ Rate of change of speed at
t = 4 s would be 5.
i.e., (d) ∴ (r).

Ques 5: A particle is moving along x-axis. Its x-coordinate varies with time as: x = -20 + 5t2 
For the given equation match the following two columns

Column I
Column II
(a) Particle will cross the origin at
(p) zero sec
(b) At what time velocity and acceleration are equal
(q) 1 s
(c) At what time particle changes its direction of motion
(r) 2 s
(d) At what time velocity is zero
(s) None

Ans: (a) → (r) (b) → (q) (c) → (s) (d) → (p)
Sol: (a) x = - 20 + 5t2 
0 = - 20 + 5t2
⇒ t = 2 s
i.e., (a) → (r).
(b) x = - 20 + 5t2
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
Velocity will be numerically equal to acceleration at t = 1 s.
Thus (b) → (q).
(c) At t = 0 s   x = - 20 m
t = 1 s              x = - 15 m
t = 2 s             x = 0 m
t = 3 s             x = + 25 m
Particle is always moving along + ive x-axis.
∴ (c) → (s).
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
∴ (d) → (p).

Ques 6: x and y-coordinates of particle movingin x - y plane are,
x = 1 - 2t + t2 and y = 4 - 4t + t2
For the given situation match the following two columns.

Column I
Column II
(a) y - component of velocity when it crosses the y-axis
(p) + 2 SI unit
(h) x - component of velocity when it crosses the x-axis
(q) - 2 SI units
(c) Initial velocity of particle
(r) + 4 SI units
(d) Initial acceleration of particle
(s) None

Ans: (a) → (q) (b) → (p) (c) → (s) (d) → (s)
Sol: (a) x = 1 - 2t + t2 
0 = 1 - 2t + t2 [for particle to cross y-axis]
i.e., t = 1 s
Y = 4 - 4t + t2
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
= - 4 + (2 x 1) [at t = 1 s]
= - 2 unit
∴ (a) → (q).
(b) Y = 4 - 4t + t2 
0 = 4 - 4t + t2 [For particle to cross x-axis]
i.e., t = 2 s
x = 1 - 2t + t2
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
= - 2 + (2 x 2) [at t = 2 s]
= + 2 unit
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
∴  Initial velocity of particle
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
i.e., (c) → (s).
DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
and  DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics
∴   Initial acceleration of particle = 2√2 unit
i.e., (d) → (s).

The document DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 | DC Pandey Solutions for JEE Physics is a part of the JEE Course DC Pandey Solutions for JEE Physics.
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FAQs on DC Pandey Solutions (JEE Advance): Motion in One Dimension- 4 - DC Pandey Solutions for JEE Physics

1. What is the significance of motion in one dimension in JEE Advanced?
Ans. Motion in one dimension is a fundamental concept in physics, and it plays a crucial role in JEE Advanced. Understanding the principles and equations related to motion in one dimension is essential for solving problems in mechanics, kinematics, and other branches of physics. It forms the basis for more complex concepts and applications in higher-level physics.
2. How can I improve my understanding of motion in one dimension for JEE Advanced?
Ans. To improve your understanding of motion in one dimension for JEE Advanced, it is important to study the fundamental concepts, equations, and principles thoroughly. Practice solving a variety of problems related to motion in one dimension to strengthen your problem-solving skills. Additionally, referring to trusted textbooks like DC Pandey's "Physics for JEE Advanced" can provide detailed explanations and examples to enhance your understanding.
3. What are some common types of problems related to motion in one dimension in JEE Advanced?
Ans. In JEE Advanced, you may come across various types of problems related to motion in one dimension. Some common types include problems involving uniform motion, accelerated motion, relative motion, projectile motion, and motion under gravity. These problems require applying the equations of motion, understanding velocity-time graphs, analyzing displacement-time graphs, and utilizing kinematic principles to arrive at the correct solutions.
4. How important is the DC Pandey JEE Advanced book for learning motion in one dimension?
Ans. The DC Pandey JEE Advanced book, particularly the chapter on motion in one dimension, is highly recommended for JEE Advanced preparation. The book offers a comprehensive coverage of the topic, including detailed explanations, solved examples, and a wide range of practice questions. It is designed to help students build a strong foundation in motion in one dimension and develop problem-solving skills required for the exam.
5. Are there any specific strategies or tips for solving motion in one dimension problems in JEE Advanced?
Ans. Yes, there are a few strategies and tips that can help you solve motion in one dimension problems effectively in JEE Advanced. First, carefully read the problem statement and identify the given information and what needs to be found. Draw a well-labeled diagram if necessary. Apply the appropriate equations of motion and kinematic principles, and solve the problem step by step. Pay attention to units, significant figures, and any special conditions mentioned in the problem. Practice regularly to improve speed and accuracy in solving these types of problems.
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