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Class 11  »  Physics  »  Kinematics

Speed and Velocity – Average and Instantaneous - UNSOLVED PRACTICE SET

Class 11

Chapter: Kinematics | Topic: Speed and Velocity Average and Instantaneous

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Class 11

SPEED AND VELOCITY – AVERAGE AND INSTANTANEOUS - UNSOLVED PRACTICE SET

Topic: Speed and Velocity Average and Instantaneous

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

Multiple Choice Questions

Q1. A car travels 120 km in 2 hours. Its average speed is:

  1. 60 km/h
  2. 240 km/h
  3. 30 km/h
  4. 120 km/h

Q2. The instantaneous velocity of a particle is defined as:

  1. Total displacement divided by total time
  2. The limiting value of average velocity as the time interval approaches zero
  3. Total distance divided by total time
  4. The velocity at the midpoint of the journey

Q3. A particle moves along a straight line with position x = t². Its instantaneous velocity at time t is:

  1. t
  2. 2t
  3. t²
  4. 2

Q4. The average velocity of a particle is zero when:

  1. The particle does not move at all
  2. The particle returns to its starting point
  3. The particle moves with constant speed
  4. The particle moves with constant acceleration

Q5. A student runs around a circular track of circumference 400 m in 80 seconds and returns to the starting point. The average velocity for this motion is:

  1. 5 m/s
  2. 0 m/s
  3. 400 m/s
  4. 80 m/s

Q6. The slope of a position-time graph at any instant gives:

  1. Average speed
  2. Instantaneous velocity
  3. Average acceleration
  4. Instantaneous acceleration

Short Answer Questions

Q7. Distinguish between speed and velocity. Is it possible for a body to have constant speed but changing velocity? Explain.

Q8. Define average velocity and instantaneous velocity. How are they related mathematically?

Q9. A car travels from city A to city B (100 km) at 50 km/h and returns from B to A at 25 km/h. Calculate the average speed and average velocity for the entire journey.

Q10. In a 100 m race at your school sports day, a runner completes the race in 12 seconds. However, the runner's position-time graph is curved, not straight. Explain why the average velocity might be different from the instantaneous velocity at any given moment.

Q11. The position of a particle is given by x(t) = 3t² − 2t + 5, where x is in metres and t is in seconds. Find the instantaneous velocity at t = 2 s.

Q12. Can the average speed of a particle be greater than the magnitude of its average velocity? If yes, give an example. If no, explain why.

Long Answer Questions

Q13. Explain the concepts of average speed, average velocity, instantaneous speed, and instantaneous velocity with suitable examples and graphs. Discuss how the slope of a position-time graph relates to velocity.

Q14. A particle moves along a straight line such that its position is given by x(t) = 2t³ − 9t² + 12t, where x is in metres and t is in seconds. Analyse the motion by finding:

(i) The initial velocity

(ii) The velocity at t = 2 s and t = 4 s

(iii) The times when the particle is momentarily at rest

(iv) The average velocity between t = 0 and t = 3 s

(v) The average speed between t = 0 and t = 3 s

Q15. Two students, Priya and Rahul, start from the same point in a park. Priya walks 100 m east in 50 seconds, then 100 m west in 50 seconds. Rahul walks 100 m east in 40 seconds, rests for 20 seconds, then walks 100 m west in 40 seconds. Compare their:

(i) Average speeds

(ii) Average velocities

(iii) Instantaneous velocities at t = 30 s

What does this comparison teach you about the difference between speed and velocity?

Application-Based Problems

Q16. A bus travels from Delhi to Agra (200 km) along a straight highway. The journey consists of three phases:

Phase 1: Travels 80 km in 1 hour

Phase 2: Stops for 30 minutes due to traffic

Phase 3: Travels the remaining 120 km in 2 hours

(a) Calculate the average speed for the entire journey.

(b) Calculate the average velocity for the entire journey (assume straight path).

(c) Calculate the instantaneous speed during Phase 1.

(d) What is the instantaneous speed during Phase 2?

(e) Plot a rough position-time graph for this journey.

Q17. The position-time graph of a particle moving along a straight line is shown below (describe verbally): From t = 0 to t = 2 s, the graph is a straight line passing through the origin with slope 4 m/s. From t = 2 s to t = 5 s, it is a horizontal line at x = 8 m. From t = 5 s to t = 7 s, it is a straight line with slope −2 m/s reaching x = 4 m.

(a) Calculate the average velocity for the entire journey (t = 0 to t = 7 s).

(b) Calculate the average speed for the entire journey.

(c) Find the instantaneous velocity at t = 1 s, t = 3 s, and t = 6 s.

(d) Describe the motion of the particle in words.

Q18. A stone is thrown vertically upward from the roof of a 20 m high building with an initial velocity of 15 m/s. It reaches the ground after some time.

(a) Calculate the maximum height reached by the stone above the ground.

(b) Calculate the total time of flight.

(c) Calculate the average velocity for the entire motion.

(d) Calculate the average speed for the entire motion.

(e) Find the instantaneous velocity just before hitting the ground.


Total: 30 Marks | Time: 40 mins

Explore more topics in Kinematics

Frame of Reference Motion in a Straight Line Position and Path Length 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