Motion in a Plane Final cet neet jee.pptx

motion in a plane

1. Motion in a Plane - Class 11 By Dr. Umesh D. Patil Rayat Shikshan Sanstha’s Annasaheb Awate College, Manchar

2. M otion Introduction to Motion Definition of Motion: A body is said to be in motion if it changes its position with respect to time, relative to a reference point. Motion Change in position over time How to understand motion effectively? Rest No change in position over time

3. Planar Motion Motion confined to a two- dimensional plane, like a flat surface. Spatial Motion Motion occurring in three- dimensional space, allowing movement in all directions. Rectilinear Motion Motion along a straight line, often seen in simple linear movements . Understanding Motion Types

4. Acceleration Vectors represent the rate of change in velocity. Importance of Vectors in Motion Velocity Vectors indicate the speed and direction of movement. Displacement Vectors show the change in position of an object.

5. 2. Rectilinear Motion (Revision) Displacement vs. Distance: Distance: The total path length traveled by an object. Displacement: The shortest distance between the initial and final positions, with direction. Calculate Displacement Shortest distance with direction Determine Start/End Identify initial and final positions Displacement Shortest distance with direction Distance Total path length traveled Understanding 𝒩otion: Distance & Displacement

6. Average Speed and Velocity Average Speed Total distance divided by total time taken. Average Velocity Total displacement divided by total time taken. Unveiling Average Speed and Velocity

7. Instantaneous Velocity Velocity at a specific instant, limit of average velocity. Instantaneous Speed Magnitude of the instantaneous velocity, a scalar quantity. Instantaneous Velocity and Speed

8. Acceleration: The rate of change of velocity with respect to time.

9. The displacement of a particle is given by s=4t 2 +2t+1. Find the velocity at t=3s. a) 26m/s b) 43m/s c) 36m/s d) 40m/s

10. The velocity of a particle is given by 𝑣=3𝑡 2 +2𝑡+4. Find the acceleration at 𝑡=2 . a) 32 m/s 2 b) 20 m/s 2 c) 14 m/s 2 d) 40 m/s 2

11. v = u + at v 2 = u 2 + 2as Understanding Equations of Motion s = ut + 1⁄2at 2 Where: v = final velocity u = initial velocity a = acceleration t = time s = displacement

12. A train starts from rest and accelerates uniformly at 2m/s 2 . What will be its velocity after 15 seconds? a) 20m /s b) 15m/s c) 30m/s d) 60m/s

13. A car accelerates from rest at 3 m/s 2 for 8 seconds. How far does it travel in this time? a) 96m b) 32m c) 64m d) 108m

14. A vehicle moving with a speed of 20m/s is brought to rest by applying brakes. If the deceleration is 5 m/s 2 , find the distance it travels before coming to rest. a) 20m b) 40m c) 30m d) 60m

15. Choose the appropriate frame of reference for velocit y analysis. Moving Frame Provides relative velocity Stationary Frame Provides absolute velocity Vector Equation:

16. Moving Train Demonstrates relative motion How to understand relative velocity in real- life scenarios? Stationary Train Provides a stable reference point

17. Motion in Two Dimensions (Vector Form) Instantaneous Velocity

18. The position of a particle is given by 𝑥=3𝑡 2 , 𝑦=4𝑡. Find the instantaneous velocity vector at t=2s, and its magnitude. a) 12 m/s b) 4 m/s c) 12.65 m/s d) 9.6 m/s

19. Instantaneous Acceleration

20. Displacement of a particle is given by 𝑠(𝑡)=t 3 −3t 2 +2t. Find the instantaneous acceleration at 𝑡=2s. a) 26 m/s 2 b) 6 m/s 2 c) 12 m/s 2 d) 20 m/s 2

21. Definition: The motion of an object thrown into the air, subject to gravity.

22. Examples: Cricket ball, basketball, bullet fired from a gun. Assumptions: Neglect air resistance, constant gravitational acceleration (g). Equations of Trajectory:

23. A projectile is fired at u=50m/s at an angle θ=45 ∘ . What is the velocity at the highest point? a) 30.25 m/s b) 35.35 m/s c) 32.60 m/s d) 36.15 m/s

24. Constant Speed Object maintains a steady speed throughout the motion. Cycle of Uniform Circular Motion Object Moves in Circle Object starts moving along a circular path. Repeat Motion The cycle continues as the object completes the circle. Changing Velocity Velocity changes direction continuously. Concept: Motion of an object along a circular path with constant speed. Note that while the speed is constant, the velocity is constantly changing direction.

25. Centripetal Force Radius (r) Circle's radius determining centripetal force. Exploring Centripetal Force Mass (m) Object's mass influencing centripetal force. Velocity (v) Object's speed affecting centripetal force.

26. A 2 kg object is moving in a circle of radius 4 meters at a speed of 3 m/s. What is the centripetal force acting on the object? a) 5 N b) 3 N c) 3.5 N d) 4.5 N

27. A small ball of mass m=0.5kg is attached to a string of length ℓ=2 mℓ=2m. It moves in a horizontal circle such that the string makes an angle 𝜃=30∘θ=30 ∘ with the vertical. Find the speed of the ball. a) 5 N b) 3 N c) 3.5 N d) 4.5 N