P2F11-Week3-Barwick

# P2F11-Week3-Barwick - P2 Week 3 Motion in One Dimension...

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P2 Week 3 Motion in One Dimension Constant acceleration Reading assignment: 2.4 and 2.5

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Kinematic Equations n The kinematic equations may be used to solve any problem involving one- dimensional motion with a constant acceleration n You may need to use two of the equations to solve one problem n The equations are useful when you can model a situation as a particle under constant acceleration
Initial time, t 0 As mentioned before, we often write the kinematic equations with t, rather than t2-t1 This is fine if the initial time, t1, can be set to 0 However, in problems with several objects that begin their motion at different times, or when a sequence of actions occur, not all equations can have t1=0. It is better to keep track of the initial time explicitly. We ` ll use the symbol t 0 to represent the initial time of the motion.

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Kinematic Equations, specific n For constant acceleration, n Can determine an object’s velocity at any time t when we know its initial velocity (v 0x at time t 0 ) and its acceleration (a x ) n Does not give any information about displacement directly v x = v 0x + a x (t - t 0 )
Kinematic Equations, specific For constant acceleration only, you do not need to use v av-x = v 0x + v x 2 v average = v = v av -x " # x # t = x 2 \$ x 1 t 2 \$ t 1 Instead, by looking at “v vs t” plot, v av can be found by Constant a v x v 0x

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Clicker question n A function f(t) changes linearly with t in the range of time between t 1 and t 2 . Let f 1 =f(t 1 ) and f 2 =f(t 2 ). What is the average value of f(t) in the range of t 1 < t < t 2 ? n A: (f 2 –f 1 )/2 n B: (f 2 +f 1 )/2 n C: (f 2 *f 1 )/2 n D: f 1 + f 2 /2 n E: None of the above f 2 f 1
Clicker question n A function f(t) changes linearly with t in the range of time between t 1 and t 2 . Let f 1 =f(t 1 ) and f 2 =f(t 2 ). What is the average value of f(t) in the range of t 1 < t < t 2 ? n Average of f(t) from t 1 to t 2 is the area under the curve from t 1 to t 2 divided by (t 2 –t 1 ) n Look at figure on board for area under curve

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Kinematic Equations, specific n For constant acceleration, n This gives you the position of the particle (x) at time t in terms of time elapsed (t–t 0 ) and initial velocity (v 0x ) and final velocity (v x at time t) n Doesn’t include acceleration x = x 0 + v av -x (t - t 0 ) x = x 0 + 1 2 v x + v 0x ( ) (t - t 0 )
Kinematic Equations, specific n For constant acceleration, n Gives final position (x at time t) in terms of initial position (x 0 at time t 0 ), initial velocity (v 0x at time t 0 ), time elapsed (t–t 0 ) and acceleration (a x ) n Doesn’t tell you about final velocity directly. x = x 0 + v 0x (t - t 0 ) + 1 2 a x (t - t 0 ) 2 v x = v 0x + a x (t - t 0 )

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Kinematic Equations, specific n For constant acceleration, n Obtained by eliminating “t-t 0 in the preceding special cases n Gives final velocity (v x when position is x) in terms of acceleration and displacement (x-x 0 ) n Does not explicitly include information about the time elapsed (t–t 0 ) v x 2 = v 0x 2 + 2 a x x " x o ( )
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P2F11-Week3-Barwick - P2 Week 3 Motion in One Dimension...

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