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Physics

Physics. “Motion in One Dimension”. Displacement and Velocity. motion - a constant change in position distance - the result of motion in any direction displacement - the result of motion in a particular direction( sign indicates direction ) scalar - a quantity having magnitude only

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Physics

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  1. Physics “Motion in One Dimension”

  2. Displacement and Velocity • motion - a constant change in position • distance - the result of motion in any direction • displacement - the result of motion in a particular direction(sign indicates direction) • scalar - a quantity having magnitude only • vector - a quantity having magnitude and direction

  3. Speed or Velocity? • speed - the time rate of change in distance • velocity - the time rate of change in displacement • Speed is a scaler. Why? • Velocity is a vector. Why? • For now, we will use the terms speed and velocity without regard to direction.

  4. Sample Problem • A runner runs 500m in 1.0 minute. What is the runners average speed in m/s? km/h? • v = Δx/t = 500m/1m(1m/60s) = 8.3m/s • Devise a conversion factor that changes m/s to km/h. • 1m/1s(1km/1000m)(60s/1m)(60m/1h) = 18/5 • To change km/h to m/s multiply by 5/18.

  5. Acceleration • acceleration - the time rate of change in velocity • a = (vf - vi ) / t • A car moving at 25m/s increases to 55m/s in 5 seconds. Find its rate of acceleration. • a = (55m/s - 25m/s)/5s = (30m/s)/5s = 6m/s2 • What does negative acceleration indicate

  6. Distance With Constant Acceleration • If an object is experiencing acceleration, the average velocity can be found by simply averaging the two velocities vi and vf. • vav = (vi + vf) / 2 • The distance can then be calculated from this average velocity by using the simple equation for distance, Δx = vt. • Δx= [(vi + vf) / 2] t

  7. Sample Problem • A racing car reaches a speed of 42m/s. It then begins a uniform negative acceleration, using its parachute and braking system, and comes to rest 5.5s later. Find how far the car moves while stopping.

  8. Velocity and Displacement with Constant Acceleration • If the constant acceleration is known, the equation rearranged to yield an equation for initial velocity. • Solve the equation for vf., a = (vf - vi)/t • If an object starts from rest, vi = 0. Given • Δx = [(vi + vf) / 2] t and vf = vi + at, derive the equation for displacement. • Δx = vi t + 1/2at2

  9. Sample Problem • A plane starting at rest at one end of a runway undergoes a constant acceleration of 4.8m/s2 for 15s before takeoff. What is the speed at takeoff? How long must the runway be for the plane to be able to take off? • Assignment: Page 69, 26-29

  10. Final Velocity After any Displacement • Using the equations for final velocity and displacement during constant acceleration, we can derive an equation for final velocity after any displacement. • Use: vf = vi + at and Δx = (vi + vf /2)t • Answer: vf2 = vi2 + 2a Δx

  11. Sample Problem • A baby sitter pushing a stroller starts from rest and accelerates at a rate of 0.500m/s2. What is the velocity of the stroller after it has traveled 4.75m? • Page 71, 30-33

  12. Falling Objects • When gravity acts on an object, the object is accelerated at the rate of 9.8m/s2, 980cm/s2 , or 32ft/s2. • These numbers are constant and should be memorized. • Any time free fall is involved, a in an equation should be replaced with g, the acceleration due to gravity.

  13. Sample Problem • A baseball is hit and remains in the air for 10 seconds. What is the maximum height of the ball? • Class Assignment: Find the height of the goal posts on the football field using a stopwatch and a baseball. • Page 74, 42-46

  14. Experiment • You will roll a ball down an incline and measure the time required for it to roll 0-10cm, 0-20cm, etc up to 0-100cm. Make three trials and average each. • Record all average values in a data table. • Plot a graph of x vs t. • Analyze the graphs with regards to constant and varying slopes. • Write a ppoc for this experiment.

  15. Plotting Graphs • 1. Identify the independent and dependent variables. • 2. Choose the appropriate range and plot the independent variable values on the x-axis and dependent on the y-axis. • 3. Decide if the origin is an appropriate point. • 4. Number and label the horizontal axis. • 5. Repeat steps 2-4 for the dependent variable. • 6. After plotting all points, draw the best fitting line through as many points as possible. • 7. Give the graph a title that best describes what it represents.

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