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Chapter 2 - Motion In One Dimention

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Published in: Physics
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Topics included: - Rest and motion - Distance - Displacement - Speed - Velocity - Acceleration

Anil N / Dehradun

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  1. Motion in One Dimension When a body moves along a straight-line path, its motion is said to be one dimensional motion. It is also called motion in a straight line or rectilinear motion. For example, the motion of a train on a straight track, a stone falling down vertically. Distance and Displacement: - The length of the path (A — C — D — B) traversed by a body is called the distance travelled by it. The shortest distance from the initial position (A) to the final position (B) of the body is called the magnitude of displacement. SI unit of both distance and displacement is meter. Speed and Velocity: - 1. 2. Speed: - a. It is the distance traveled per unit of time. It is how fast an object is moving. b. It is a scalar quantity. c. Speed (s) = DistanceÆime d. Its SI unit is m s- Velocity: - a. It is a measure of how fast something moves in a particular direction. b. It is a vector quantity. c. Velocity = Displacement(S) / Time (t) d. Its SI unit is m s-1 Acceleration. l. It is the rate of change of velocity per unit time. 2. It is a vector quantity. 3. If the velocity of the body increases with time, the motion is said to be accelerated, if the velocity of the body decreases with time, the motion is said to be retarded. 4. Acceleration = Change in Velocity/Time Interval Graphical Representation of Linear Motion: - The graphs of linear motion are used to show displacement at a particular time at a particular velocity.
  2. Example, on a displacement-time graph, straight lines indicate constant velocity and curved lines indicate acceleration. Displacement Time Graphical Representation: - Case a: Displacement time graph of a stationary object is a straight line parallel to the time axis • Case b: Displacement time graph of a body moving with uniform velocity is a straight line inclined • to the time axis The velocity can be obtained by finding the slope of the straight line. Case c: • Displacement time graph of a body moving with variable velocity is a curve. The velocity at any instant can be obtained by finding the slope of the tangent drawn to the curve for that instant of time. Time (a) Equations of Motion: - Time (b) Time (c) Equations of motion are equations that describe the behavior of a physical system in terms of its motion as a function of time. 1. First equation of motion: Acceleration a = Hence, v = u + at. 2. Second equation of motion: s — — u)t + ut
  3. Or, s = ut+ —at 3. Third equation of motion: v2_ u2 = 2as

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