Notes on Motion in a Straight Line (Class 11 Physics)

1. Mechanics

Mechanics is the branch of Physics dealing with the motion of physical objects and the forces acting upon them. It is broadly categorized into three branches:

  • Statics: The study of objects at rest and the forces in equilibrium.
  • Kinematics: The study of the motion of objects without considering the forces causing the motion.
  • Dynamics: The study of the forces and torques that cause or change the motion of objects.

2. Rest and Motion

  • Rest: An object is said to be at rest if its position does not change with respect to its surroundings. For example, a whiteboard in a classroom is at rest relative to the classroom.
  • Motion: An object is in motion if it changes its position relative to its surroundings. For instance, a person walking is in motion relative to the ground.
  • Relative Nature: Rest and motion are relative terms. The same object may appear at rest in one reference frame and in motion in another. For example, a passenger in a moving car is at rest relative to the other passengers but in motion relative to a person standing outside the car.

3. Point Mass and Rectilinear Motion

  • Point Mass: For simplicity, objects are often treated as point masses if their size is negligible compared to the distances they travel.
  • Rectilinear Motion: The study of objects moving along a straight line. In this chapter, motion is considered only in a straight line.

4. Position, Distance, Displacement

  • Position: Defined with respect to a reference point or origin.
  • Distance: The total length of the path traveled by an object. It is a scalar quantity with SI unit meters (m) and dimensions [M^0L^1T^0].
  • Displacement: The change in position of an object, represented as the difference between final and initial positions. It is a vector quantity with SI unit meters (m) and dimensions [M^0L^1T^0].

Differences Between Distance and Displacement:

  • Distance is a scalar and is always positive. Displacement is a vector and can be positive, negative, or zero.
  • Distance measures the total path length traveled, while displacement measures the shortest path between initial and final positions.

Differences Between Speed and Velocity:

  • Speed is a scalar quantity that measures how fast an object is moving, with SI unit meters per second (m/s). Velocity is a vector quantity that includes both speed and direction, with SI unit meters per second (m/s).

Note: For motion in a straight line and same direction, the magnitude of displacement equals the total path length, and average velocity equals average speed.

5. Scalar and Vector Quantities

  • Scalar Quantities: Physical quantities with only magnitude and no direction (e.g., mass, length, time, distance, speed).
  • Vector Quantities: Physical quantities with both magnitude and direction (e.g., displacement, velocity, acceleration, force).

6. Average Velocity and Average Speed

  • Average Velocity: Defined as the displacement divided by the time interval. Its SI unit is meters per second (m/s) and its dimensions are [M^0L^1T^−1].
  • Average Speed: Defined as the total path length divided by the total time interval. Its SI unit is meters per second (m/s) and its dimensions are [M^0L^1T^−1].

7. Instantaneous Velocity and Instantaneous Speed

  • Instantaneous Velocity: The velocity of an object at a particular instant, defined as the limit of the average velocity as the time interval approaches zero: v=limΔt0ΔxΔt=dxdtv = \lim_{\Delta t \to 0} \frac{\Delta x}{\Delta t} = \frac{dx}{dt} Its SI unit is meters per second (m/s) and its dimensions are [M^0L^1T^−1].
  • Instantaneous Speed: The magnitude of instantaneous velocity. Its SI unit is meters per second (m/s) and its dimensions are [M^0L^1T^−1].

8. Acceleration

  • Average Acceleration: Defined as the change in velocity divided by the time interval:

    a=v2v1t2t1a = \frac{v_2 – v_1}{t_2 – t_1}Its SI unit is meters per second squared (m/s²) and its dimensions are [M^0L^1T^−2].

  • Instantaneous Acceleration: The acceleration at a particular instant, defined as:

    a=limΔt0ΔvΔt=dvdta = \lim_{\Delta t \to 0} \frac{\Delta v}{\Delta t} = \frac{dv}{dt}Its SI unit is meters per second squared (m/s²) and its dimensions are [M^0L^1T^−2].

Note: In this chapter, acceleration is considered constant. The equations of motion under constant acceleration are:

  • v=v0+atv = v_0 + at
  • S=v0t+12at2S = v_0 t + \frac{1}{2} a t^2
  • v2v02=2aSv^2 – v_0^2 = 2aS
  • S=v0+v2tS = \frac{v_0 + v}{2} t

9. Graphs

  • Uniform Motion: For uniform motion (constant velocity), the position-time graph is a straight line with zero slope for acceleration. Velocity-time graph is a horizontal line (constant velocity) and acceleration-time graph is a horizontal line at zero (no acceleration).
  • Non-Uniform Motion: For uniformly accelerated motion, the position-time graph is a parabola. The velocity-time graph is a straight line with a slope equal to acceleration. The acceleration-time graph is a horizontal line at constant acceleration.

Note: In uniformly accelerated motion, the rate of change of velocity is constant.

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