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Motion in a Plane Final cet neet jee.pptx
- 1. Motion in a Plane- Class 11 By Dr. Umesh D. Patil Rayat Shikshan Sanstha’s Annasaheb Awate College, Manchar
- 2. Motion 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 atwo- 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 rateof 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 Displaceme nt Shortest distance with direction Determi ne Start/En d Identify initial and final positions Displacement Shortest distance with direction Distanc e Total path length traveled Understanding otion: 𝒩 Distance & Displacement
- 6. Average Speed and Velocity Average Speed Totaldistance 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 specificinstant, limit of average velocity. Instantaneous Speed Magnitude of the instantaneous velocity, a scalar quantity. Instantaneous Velocity and Speed
- 8. •Acceleration: The rateof change of velocity with respect to time. Acceleration is calculated The Cycle of Acceleration NewVelocity Velocity Change Velocity is updated Velocity increases or decreases Acceleration Occurs Time Elapsed Time passes during velocity change
- 9. The displacement ofa particle is given by s=4t2 +2t+1. Find the velocity at t=3s. a) 26m/s b) 43m/s c) 36m/s d) 40m/s
- 10. The velocity ofa particle is given by =3 𝑣 𝑡2 +2 +4. Find the acceleration at 𝑡 =2 . 𝑡 a) 32 m/s2 b) 20 m/s2 c) 14 m/s2 d) 40 m/s2
- 13. v = u+ at v2 = u2 + 2as Understanding Equations of Motion s = ut + 1⁄2at2 Where: • v = final velocity • u = initial velocity • a = acceleration • t = time • s = displacement
- 14. A train startsfrom rest and accelerates uniformly at 2m/s2 . What will be its velocity after 15 seconds? a) 20m/s b) 15m/s c) 30m/s d) 60m/s
- 15. A car acceleratesfrom rest at 3 m/s2 for 8 seconds. How far does it travel in this time? a) 96m b) 32m c) 64m d) 108m
- 16. A vehicle movingwith a speed of 20m/s is brought to rest by applying brakes. If the deceleration is 5 m/s2 , find the distance it travels before coming to rest. a) 20m b) 40m c) 30m d) 60m
- 17. Choose the appropriateframe of reference for velocity analysis. Moving Frame Provides relative velocity Stationary Frame Provides absolute velocity • Vector Equation:
- 18. Moving Train Demonstrates relative motion Howto understand relative velocity in real-life scenarios? Stationary Train Provides a stable reference point
- 19. 4. Motion inTwo Dimensions (Vector Form) Instantaneous Velocity
- 20. The position ofa particle is given by =3 𝑥 𝑡2 , =4 . Find the instantaneous 𝑦 𝑡 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
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- 22. Displacement of aparticle is given by ( )=t 𝑠 𝑡 3 −3t2 +2t. Find the instantaneous acceleration at =2s. 𝑡 a) 26 m/s2 b) 6 m/s2 c) 12 m/s2 d) 20 m/s2
- 23. Definition: The motionof an object thrown into the air, subject to gravity.
- 24. • Examples: Cricketball, basketball, bullet fired from a gun. • Assumptions: Neglect air resistance, constant gravitational acceleration (g). • Equations of Trajectory:
- 25. A projectile isfired 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
- 26. Constant Speed Object maintainsa 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.
- 28. Centripet al Force Radius (r) Circle's radius determiningcentripetal force. Exploring Centripetal Force Mass (m) Object's mass influencing centripetal force. Velocity (v) Object's speed affecting centripetal force.
- 29. A 2 kgobject 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
- 31. A small ballof 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 =30 θ=30 𝜃 ∘ ∘ with the vertical. Find the speed of the ball. a) 5 N b) 3 N c) 3.5 N d) 4.5 N