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Rectilinear Motion Continued Sections 4.2 and 4.3

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Updates & Reminders The date and time of the final: Thursday, December 11 from 10 a.m. to 12 p.m. MLT 208. There is no lab this week. Test #1 will take place on Thursday, 9/18. Test covers Chapters 1, 3, and 4 (only constant motion), Galileo, Knowledge & Faith, graphing) There is no Mallard-based reading quiz prior to class on Thursday.

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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 = x o + vt (equation 1) Solving practical problems…

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Sample Problems An industrial sewing machine can stitch cloth at a rate of 3.8cm/s. During an 8- hour continuous run, how many METERS of stitching can be accomplished? The current men's world record for the 100-meter dash is 9.58s. Usain Bolt from Jamaica set the record on August 16, 2009 at the World Championships in Berlin, Germany. What was Bolt’s average speed over this interval? A lightning flash occurs and thunder is heard 2.4s later. How far away was the lightning bolt at its nearest point? Assume that the speed of sound is 343m/s. Be aware that the speed of light is so high that it can travel around Earth 7.5 times in one second. In the above question, if the thunder continues to rumble for another 3.9s after the start, what was the most distant part of the lightning bolt? A surface ship is bouncing sonar waves off the ocean bottom to determine depth. If a “ping” takes 1.534s to go down and return, how deep is the ocean beneath the ship? Assume that speed of the sonar wave is 1,473m/s.

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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 + velocity o v = v o + at(equation 2) Solving a practical problem…

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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.

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Uniform Acceleration V-T Graphs The relationship between variables in uniformly accelerated motion. – x = x o +v o t + ½ at 2 – 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.

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Kinematic Relationships x = x o + vt (constant velocity) (equation 1) v = v o + at (equation 2) x = x o + v o t + ½at 2 (equation 3) Substituting t from equation 2 into equation 3 results in 2aΔx = v 2 – v o 2 (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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Mathematical Model of Motion Chapter 5. Velocity Equations Average velocity: v = d/ t To find the distance traveled with constant or average velocity.

Mathematical Model of Motion Chapter 5. Velocity Equations Average velocity: v = d/ t To find the distance traveled with constant or average velocity.

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