Ch 02 Kinematics in One Dimension

Ch 02 Kinematics in One Dimension - LECTURE NOTE 2...

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LECTURE NOTE 2 Kinematics in One Dimension The motion of a “particle” is completely specified if the particle’s position in space is known at all times . Consider a car (which we treat as a particle ) moving along the x axis from a point P to a point Q as shown where the indices i and f refer to the initial and final values. x - x P Q + x x =0 x i x f The displacement x is computed by subtracting the initial position x i from the final position x f . Displacement Kinematics deals with the concepts that are needed to describe motion. Dynamics deals with the effect that forces have on motion. Together, kinematics and dynamics form the branch of physics known as Mechanics.
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x t i t f x f Q P Q Slope=v x x x i x f x i P t A car moving to the right along a O t i t f t straight line taken to be the x -axis . Because we are interested only in Position-time graph the car’s translational motion , we for the motion of a “ particle can treat it as a “ particle ”. The change in the position of the particle is the displacement x defined as: x x f x i For “anything”, we always take the final value minus the original value . x is positive or negative according to x f x i or x f x i , respectively . Displacement should not be confused with the distance traveled ” , since the distance traveled for any motion is clearly positive . It is almost impossible to talk about motion without using words, such as velocity and speed.
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The average velocity v of the particle is defined as the ratio of its displacement x and the time interval t : i f i f t t x x t x v Dimensions : L / T (length divided by time ) . SI Units : m / s . v is independent of the path taken between the points P and Q . It depends only on the initial and final coordinates of the particle. i f i f t t x x t x v If a particle starts at some point and returns to the same point via any path , its average velocity for this trip is zero ( because x = 0 ) . Average velocity gives us no details of the motion between points P and Q. v of a particle in one dimension can be positive or negative , depending on the sign of the displacement x while the time interval t is always positive. Average Velocity v Displacement Average velocity Elapsed time
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v of a particle during the time interval t i to t f is equal to the slope of the straight line joining the initial and final points on the space-time graph. Slope represents the ratio of the change in the quantity represented on the vertical axis to the change in the quantity represented on the horizontal axis. v = 2 m/s 3 m 3 m 1 m/s ?
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