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Rectilinear Motion Continued

Rectilinear Motion Continued. Sections 4.2 and 4.3. The Position-Time graph (P-T ). Slope is velocity (+/- speed) y-intercept is position at time = 0 y = mx + b (algebraic relationship) distance = velocity*time + distance o x = vt + x o (equation 1)

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Rectilinear Motion Continued

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  1. Rectilinear Motion Continued Sections 4.2 and 4.3

  2. The Position-Time graph (P-T) • Slope is velocity (+/- speed) • y-intercept is position at time = 0 • y = mx + b (algebraic relationship) • distance = velocity*time + distanceo • x = vt + xo (equation 1) • Solving a practical problem…

  3. The Velocity-Time Graph • Slope = change in velocity / change in time which is acceleration • y-intercept equals velocity at time = 0 • y = mx + b • velocity = acceleration*time + velocityo • v = vo + at (equation 2) • Solving a practical problem…

  4. The V-T graph details • Constant (non-accelerated) motion • Slope = zero • Uniformly accelerated motion • Slope constant, but does not equal zero • Non-uniformly accelerated motion • Slope of tangent line at a given point gives accel. • One cannot determine initial position based on a V-T graph. • The area under a V-T graph is displacement.

  5. Uniform Acceleration V-T Graphs • The relationship between variables in uniformly accelerated motion. • x = xo+vot + ½ at2 • A practical example… • We will address this subject matter further in Chapter 6. • This week’s reflection will be based on a reading of the transitional Chapter 5.

  6. Kinematic Relationships • x = xo + vt (constant velocity) (equation 1) • v = vo + at (equation 2) • x = xo + vot + ½at2 (equation 3) • Substituting t from equation 2 into equation 3 results in 2aΔx = v2 – vo2 (equation 4) • Extra credit project for one point: • Demonstrate the derivation of equation 4. • Turn in written proof on Thursday at start of class.

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