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Class 11  ยป  Physics  ยป  Kinematics

Motion in a Straight Line โ€“ Position and Path Length - UNSOLVED PRACTICE SET

Class 11

Chapter: Kinematics | Topic: Motion in a Straight Line Position and Path Length

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Study Material.
Class 11

MOTION IN A STRAIGHT LINE โ€“ POSITION AND PATH LENGTH - UNSOLVED PRACTICE SET

Topic: Motion in a Straight Line Position and Path Length

Time: 40 mins | Marks: 30 | Difficulty: Medium

Multiple Choice Questions

Q1. The position of a particle moving along a straight line is given by x = 3tยฒ + 2t, where x is in metres and t is in seconds. The position of the particle at t = 0 is:

  1. 0 m
  2. 2 m
  3. 3 m
  4. 5 m

Q2. A student walks from point A to point B along a straight path of length 100 m and then returns to point A. The path length and displacement are respectively:

  1. 100 m and 100 m
  2. 200 m and 0 m
  3. 0 m and 200 m
  4. 100 m and 0 m

Q3. Path length is a:

  1. Vector quantity
  2. Scalar quantity
  3. Neither scalar nor vector
  4. Sometimes scalar and sometimes vector

Q4. A particle moves from x = 2 m to x = 8 m and then to x = 5 m along a straight line. The displacement of the particle is:

  1. 11 m
  2. 3 m
  3. 5 m
  4. 15 m

Q5. The magnitude of displacement of a particle is always:

  1. Greater than the path length
  2. Equal to the path length
  3. Less than or equal to the path length
  4. Zero

Q6. A runner completes one full lap around a circular track of radius 50 m and returns to the starting point. The displacement and path length are:

  1. 0 m and 0 m
  2. 0 m and 100ฯ€ m
  3. 100ฯ€ m and 0 m
  4. 100 m and 100ฯ€ m

Short Answer Questions

Q7. Distinguish between position, displacement, and path length. Illustrate with a simple example.

Q8. A student walks 3 km east, then 4 km north, and finally 3 km west. Calculate the total path length and the displacement from the starting point.

Q9. The position-time graph of a particle is a straight line parallel to the time axis. What does this indicate about the motion of the particle?Q. Type your question here...

Q10. In your school playground, you walk from the basketball court to the volleyball court (50 m east), then to the cricket pitch (30 m north), and finally back to the basketball court. Calculate your total path length and displace

Q11. Can the displacement of a particle be zero even when the path length is not zero? Explain with an example.

Q12. The position of a particle is given by x(t) = 5 + 2t โˆ’ tยฒ, where x is in metres and t is in seconds. Find the position of the particle at t = 0, t = 1 s, and t = 3 s.

Long Answer Questions

Q13. Explain the concepts of position, path length, and displacement with suitable diagrams. Discuss the relationship between these quantities and explain when they are equal and when they differ.

Q14. A particle moves along the x-axis according to the equation x(t) = 2tยณ โˆ’ 15tยฒ + 36t + 5, where x is in metres and t is in seconds. Analyse the motion by finding:

(i) The initial position of the particle

(ii) The times when the particle is at rest

(iii) The displacement of the particle between t = 0 and t = 5 s

(iv) The total path length travelled by the particle between t = 0 and t = 5 s

Q15. Three friends โ€” Aman, Bharat, and Chetan โ€” start from the same point in a park. Aman walks 4 m east, Bharat walks 3 m north, and Chetan walks 5 m in a direction such that he ends up at the same point as Aman. Analyse their journeys in terms of position, displacement, and path length. What does this tell you about the relationship between displacement and the actual path taken?

Application-Based Problems

Q16. A delivery robot moves along a straight corridor in a school. Its position at various times is recorded as follows:

At t = 0 s, x = 0 m

At t = 2 s, x = 8 m

At t = 4 s, x = 16 m

At t = 6 s, x = 12 m

At t = 8 s, x = 20 m

(a) Calculate the displacement of the robot between t = 0 and t = 8 s.

(b) Calculate the total path length travelled by the robot.

(c) Calculate the displacement between t = 4 s and t = 6 s. What does the negative sign (if any) indicate?

(d) Plot a rough position-time graph for this motion.

Q17. A train travels from Delhi to Jaipur (280 km) and then returns to Delhi. On the onward journey, it stops at Gurgaon (30 km from Delhi), Rewari (90 km from Delhi), and Alwar (160 km from Delhi) before reaching Jaipur. On the return journey, it takes a different route via Ajmer, covering a total distance of 320 km.

(a) Calculate the total path length for the entire journey.

(b) Calculate the displacement for the entire journey.

(c) A passenger boards at Gurgaon and alights at Alwar. Calculate the passenger's displacement and path length.

(d) Explain why the train's displacement is different from its path length.

Q18. An ant crawls along the edge of a rectangular table of length 2 m and breadth 1 m. It starts from one corner, moves along the length, then the breadth, then returns along the diagonal to the starting point.

(a) Calculate the total path length travelled by the ant.

(b) Calculate the displacement of the ant for the entire journey.

(c) At what point during the journey is the ant's displacement equal to its path length?

(d) Draw a diagram showing the ant's path and indicate the displacement vector.


Total: 30 Marks | Time: 40 mins

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Frame of Reference Speed and Velocity Average and Instantaneous Acceleration Kinematic Equations for Uniform Acceleration Relative Velocity Motion in a Plane Scalars and Vectors Vector Addition Triangle and Parallelogram Law Resolution of Vectors and Unit Vectors Projectile Motion Uniform Circular Motion