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Physics

Rest and Motion: Kinematics

Relative Velocity

Class 11
⚡ Quick Summary
The velocity of an object as seen from another moving object is called relative velocity. It's like observing the world from a different moving frame of reference. To find the relative velocity of A with respect to B, subtract the velocity of B from the velocity of A.
v<sub>A,B</sub> = v<sub>A</sub> - v<sub>B</sub>
  • Relative Velocity Formula: vA,B = vA - vB, where vA,B is the velocity of A with respect to B, vA is the velocity of A with respect to the ground, and vB is the velocity of B with respect to the ground.
  • This formula applies to both one-dimensional and two-dimensional motion (using vector subtraction).

Relative Motion and Acceleration

Class 11
⚡ Quick Summary
When observing the motion of an object from different moving frames of reference, the acceleration of the object can appear different. If two frames, S1 and S2, observe the same particle with accelerations of equal magnitude, it tells us something about how the frames are moving relative to each other. If the magnitudes of acceleration are equal, the relative acceleration between the frames could be 0 or a maximum of twice the individual accelerations.
|a_relative| = |a2 - a1|, 0 <= |a_relative| <= |a1| + |a2|
  • Frames of reference S1 and S2.
  • Acceleration of a particle as seen from S1: a1
  • Acceleration of a particle as seen from S2: a2
  • Given: |a1| = |a2| = 4 m/s²
  • (a) Frames at rest: Not necessarily true.
  • (b) Frames moving with constant relative velocity: Not necessarily true.
  • (c) The acceleration of S2 with respect to S1 may either be zero or 8 m/s². This is possible. The relative acceleration could range from 0 (if both frames have the same acceleration) to 8 m/s² (if their accelerations are in opposite directions).
  • (d) The acceleration of S2 with respect to S1 may be anything between zero and 8 m/s². This is the correct statement. The relative acceleration depends on the directions of a1 and a2.

Distance and Displacement

Class 11
⚡ Quick Summary
Distance is the total length of the path traveled. Displacement is the shortest distance between the initial and final positions, with a direction.
Distance = Sum of all path lengths. Displacement = Final Position - Initial Position
  • Distance: Total path length covered by an object. It's a scalar quantity.
  • Displacement: The shortest distance between the initial and final positions. It's a vector quantity (has magnitude and direction).

Average Speed and Average Velocity

Class 11
⚡ Quick Summary
Average speed considers the total distance traveled over time. Average velocity considers the overall displacement over time.
Average Speed = Total Distance / Total Time. Average Velocity = Total Displacement / Total Time
  • Average Speed: Total distance traveled divided by the total time taken. It's a scalar quantity.
  • Average Velocity: Total displacement divided by the total time taken. It's a vector quantity.

Average Acceleration

Class 11
⚡ Quick Summary
Average acceleration is the change in velocity over a period of time.
Average Acceleration = (Final Velocity - Initial Velocity) / Time
  • Average Acceleration: Change in velocity divided by the time interval during which the change occurs. It's a vector quantity.

Graphical Representation of Motion

Class 11
⚡ Quick Summary
Graphs like speed-time or position-time graphs can visually show how an object is moving. The slope and area under the graph give valuable information about velocity, acceleration, and distance.
Area under velocity-time graph = displacement. Slope of velocity-time graph = acceleration
  • Speed-time graph: Shows the speed of an object as a function of time. The area under the curve represents the distance traveled.
  • Position-time graph: Shows the position of an object as a function of time. The slope of the graph represents the velocity.
  • Velocity-time graph: The area under the curve represents the displacement. The slope of the graph represents the acceleration.

Instantaneous Velocity

Class 11
⚡ Quick Summary
Instantaneous velocity is the velocity of an object at a specific moment in time.
v = lim (Δx/Δt) as Δt approaches 0
  • Instantaneous Velocity: The velocity of an object at a particular instant in time. It is the limit of the average velocity as the time interval approaches zero. On a position-time graph, it's the slope of the tangent line at that instant.