Chapter03 - Graphs of the motion with constant acceleration...

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Graphs of the motion with constant acceleration
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± Example) The figure shows a plot of v x ( t ) for a car traveling in a straight line. (a) What is a av,x between t = 6 s and t = 11 s ? (b) What is v av,x for the same time interval? (c) What is v av,x for the interval t = 0 to t = 20 s ? (d) What is the increase in the car’s speed between 10 and 15 s ? (e) How far does the car travel from time t = 10 s to time t = 15 s ?
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Chapter 3 : Motion in Two or Three Dimensions
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± Motion of a particle in space ² Position : ² Displacement : ² Average velocity: ² Instantaneous velocity 1. Position and Velocity Vectors ˆ ˆˆ rx iy j z k = ++ r av r v t Δ = Δ r r 0 lim ˆ t rd r v td t dx dy dz ij k dt dt dt Δ→ Δ == Δ =+ + r r r () ,, , , xyz dx dy dz vv v v dt dt dt ⎛⎞ ⎜⎟ ⎝⎠ r 222 xy z v vvv = r 21 rrr Δ =− r rr
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± A velocity in the xy -plane can be decomposed into separate x and y components. ± Trigonometry will aid the determination.
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2. Acceleration Vector ± Average acceleration: ± Instantaneous acceleration av v a t Δ = Δ r r 0 lim ˆ ˆˆ t y x z vd v a td t dv dv dv ij k dt dt dt Δ→ Δ == Δ =+ + r r r () 22 2 222 ,, , , , , y x z xyz dv dv dv dx d y
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Chapter03 - Graphs of the motion with constant acceleration...

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