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Motion

Motion. Topics. Learning Objectives:. Introduction to Equation of Motion. Equation for Velocity Time Relation. Equation for Position Time Relation. Equation for Position Velocity Relation. Motion. Introduction to Equations of Motion.

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Motion

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  1. Motion Topics Learning Objectives: Introduction to Equation of Motion Equation for Velocity Time Relation Equation for Position Time Relation Equation for Position Velocity Relation

  2. Motion Introduction to Equations of Motion When an object moves along a straight line with uniform acceleration, then relation between velocity, acceleration during motion and the distance covered by it in a certain time interval by a set of equations known as the equations of motion.

  3. Motion Introduction to Equations of Motion There are three such equations: Where u is the initial velocity of the object which moves with uniform acceleration ‘a’ for time t, v is the final velocity, and ‘s’ is the distance traveled by the object in time ‘t’. These three equations can be derived by graphical method.

  4. Motion • Equation for Velocity-Time Relation Consider the velocity-time graph of an object that moves under uniform acceleration. Suppose an object moving with initial velocity OA=u, And its final velocity is BC=v change in velocity BD=BC – CD time is OC=t.

  5. Motion • Equation for Velocity-Time Relation

  6. Motion Equation for Position-Time Relation Let us consider that the object has travelled a distance ‘s’ in time t under uniform acceleration ‘a’. The distance travelled by the object is obtained by the area enclosed within OABC under the velocity-time graph AB. AreaOABC of trapezium = area of the rectangle OADC + area ofthe triangle ABD

  7. Motion Equation for Position-Time Relation

  8. Motion Equation for Position–VelocityRelation The distance ‘s’ travelled by the object in time t, moving under uniform acceleration ‘a’ is given by the area enclosed within the trapezium OABC under the graph. That is, s = area of the trapezium OABC

  9. Motion Equation for Position–VelocityRelation Substituting OA=u, BC = v and OC = t, we get

  10. Motion Equation for Position–VelocityRelation From the velocity time relation we get Using Eqs. and we have

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