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Acceleration 1D motion with Constant Acceleration Free Fall Lecture 04 (Chap. 2, Sec. 6-10 ) General Physics (PHYS101) Sections 30 and 33 are canceled and became section 27

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Lightning Review Displacement - change of position Average velocity - displacement over time interval Instantaneous velocity - the same but for very small time interval Last lecture:

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Average Acceleration Average acceleration is the rate of change of the velocity Changing velocity (non-uniform) means an acceleration is present Average acceleration is a vector quantity (i.e described by both magnitude and direction) SI unit: m/s 2

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Instantaneous Acceleration Instantaneous acceleration is the limiting case of the average acceleration as the time interval goes to zero.

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Graphical Interpretation of Acceleration Average acceleration is the slope of the line connecting the initial and final velocities on the velocity-time graph Instantaneous acceleration is the slope of the tangent to the curve of the velocity-time graph for the given value of time

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1D motion: uniform velocity Uniform velocity (shown by red arrows maintaining the same size) Acceleration equals zero

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1D motion: constant (positive) acceleration Velocity and acceleration are in the same direction Acceleration is uniform (blue arrows maintain the same length) Velocity is increasing in time (red arrows are getting longer)

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1D motion: constant (negative) acceleration Velocity and acceleration are in opposite directions Acceleration is uniform (blue arrows maintain the same length) Velocity is decreasing (red arrows are getting longer)

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1D motion: constant acceleration Our job: to find the equation for the position and velocity of the object to make predictions!

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10 1D motion with constant acceleration Recall that We know that We find v t v0v0 Since x t x0x0

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11 1D motion with constant acceleration

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12 Summary of kinematic equations: 1D motion acceleration is constant displacement as a function of velocity and time displacement as a function of time velocity as a function of time velocity as a function of displacement average velocity Displacement as a function of velocity

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13 Free fall - 1D motion with constant acceleration

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14 Free fall - 1D motion with constant acceleration 0 x 1 2 3 0 y 1 2 3 All objects moving under the influence of only gravity are said to be in free fall All objects falling near the earth’s surface fall with a constant acceleration This acceleration is called gravitations acceleration, indicated by g and always points perpendicular to the earth’s surface y

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15 acceleration displacement vs velocity and time displacement vs time velocity vs time velocity vs displacement average velocity displacement vs velocity Free fall - 1D motion with constant acceleration

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16 Case 1: zero initial velocity y

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17 Case 2: NONzero initial velocity y y Case 1 Case 2

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18 Case 3: object thrown upward

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19 Case 4: object thrown upward

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Free fall Mass does not matter, if the air resistance is neglected

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21 Positive acceleration

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22 Negative acceleration

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23 1D motion with constant acceleration Example 1: A car is traveling with a constant speed v 0. At some time, the driver puts on the brakes, which slows the car down at a rate of a. Find: how much farther does the car travel for time t f, before it stops completely. low long does it travel if the stopping distance is x f. Given: v 0 =v 0 a=-a x 0 =0 t 0 =0 v=0 Find: 1) x f =?, knowing t f. 2) t f =?, knowing x f.

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