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Understanding 1D Kinematics: Position, Velocity, and Acceleration in Motion

Learn about position, displacement, velocity, and acceleration in 1D motion and solve problems related to uniformly accelerated motion and graphical relationships between x, v, and a.

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Understanding 1D Kinematics: Position, Velocity, and Acceleration in Motion

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  1. Ch1: 1D Kinematics Recall main points: position, displacement, velocity and acceleration (geometrically and algebraically) Discuss Pre-lecture and Check Points Examples of problems

  2. 1.1 Main Points Position x of point P in 1D: Axis, Origin, Direction Average velocity of P between times t1 and t2: Instantaneous Velocity of P at time t: Instantaneous acceleration of P at t:

  3. 1.1 Main Points Uniformly Accelerated motion (motion with a=cst): Let’s assume a quadratic relationship between x and t (all coeffcst): We compute first the velocity and thus the 1st derivative of x(t) /t: And then 2nd derivative to get a: Meaning of the coef. a : a=1/2a Meaning of the coef. b and g. They depend on v and x at t=0 : At t=0: and: So that we define initial position and initial velocity: Algebraic relationship from x to v to a. General case for 1 D motion with constant acceleration:

  4. 1.1 Main Points Graphical relationship from x to v to a. Example start with a=cst Given “a” : find “v” then “x”: v a • A v=10 m/s t t=5s t=1s v=-2 m/s • B t -2m/s2 • C x • D • 1 • 2 • E MORE THAN 1 CORRECT ANSWER t=5s t • F NPA • 4 • 3 • 5 2, 3 and 4 • 6 2 and 3

  5. 1.2 Discuss CheckPoint 2: Att = 0a ball, initially at rest, starts to roll down a ramp with constant acceleration. Suppose it moves1 m betweent = 0secandt = 1 sec.How far does it move betweent = 1 secandt = 2 sec? Set up problem (always same way ): Picture: Axes with origin and direction Equations relevant to problem and specified for axis choice Constraint Equations Solution

  6. 1.3 problems Relative signs of v, a and relation to speed and slowing down or speeding up. Difference between the quantity and its magnitude.

  7. 1.3 problems Example. Throw an object up in the air. A. How high does it go above release point, given vo?

  8. 1.3 problems Example. Throw an object up in the air, cont’d B. How long does it stay in the air, given vo?

  9. 1.3 problems Example. Two objects up in the air. Released same time, one from h at vo=0, the other from y=0 at voAfter how long do they meet?

  10. 1.3 problems Example.

  11. Ch 1: Assignments

  12. Ch 1: Assignments

  13. Ch 1: Assignments

  14. Ch 1: Assignments

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