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Constant acceleration
Constant velocity Constant acceleration a, m/s2 t, s v, m/s x, m a, m/s2 t, s v, m/s x, m
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constant acceleration
Position vs Time constant acceleration x, m t, s 0.5 1.0 1.5 2.0 2.5 1 2 3 4 5 6 x~t2 ?
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Velocity vs Time Displacement?
Use the graph to find the object’s displacement from 0sec to 2sec v, m/s 6 5 4 3 Use the graph to find the object’s displacement from 0sec to 4sec 2 1 1 2 3 4 5 t, s Use the graph to find the object’s displacement from 2sec to 5sec
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Velocity vs Time 9 meters Displacement? t, s v, m/s 6 5 4 3 2 1 1 2 3
1 2 3 4 5 t, s
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Velocity vs Time 15 meters Displacement? t, s v, m/s 1 2 3 4 5 6 1 2 3
1 2 3 4 5 t, s
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Velocity vs Time 13.75 meters Displacement? t, s v, m/s 6 5 4 3 2 1 1
1 2 3 4 5 t, s
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Velocity vs Time 12.5 meters Displacement? t, s v, m/s 1 2 3 4 5 6 1 2
1 2 3 4 5 t, s
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Velocity vs Time Displacement? v=at v, m/s 5a ? ? 1 2 3 4 5 t, s
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Velocity vs Time v=at X = ½ at2 aT 5a ½ 25a ½ aT2 T t, s t, s v, m/s
1 2 3 4 5 T t, s x, m t, s 0.5 1.0 1.5 2.0 2.5 1 2 3 4 5 6
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vf - vi = at x = vit + ½ at2 vf X2 = ½ (vf – vi)T X2 = ½ aT2 X1 = viT
acceleration = change in velocity time vf - vi = at v, m/s vf X2 = ½ (vf – vi)T X2 = ½ aT2 X1 = viT X1 vi X = X1 + X2 = viT + ½ aT2 T t, s x = vit + ½ at2 Check the units! Check the limiting cases! Xtrain + Xboy a vi = const
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vf - vi = aT vf X2 X2 = ½ (vf – vi)T X1 X1 = viT vi
acceleration = change in velocity time v, m/s vf - vi = aT vf X2 X2 = ½ (vf – vi)T X1 X1 = viT vi X = X1 + X2 =vi T + ½ (vf – vi)T X = ½ (vf + vi)T T = (vf-vi)/a T t, s X = (vf2– vi2) 2a a≠0! Check the units! Check the limiting cases! 2aX = (vf2– vi2)
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A ball is thrown straight up. At the top of its trajectory, its
velocity is zero, acceleration is zero. velocity is non-zero, acceleration is non-zero. velocity is zero, acceleration is non-zero. velocity is non-zero, acceleration is zero.
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This graph shows velocity as a function of time for a car of mass 1
This graph shows velocity as a function of time for a car of mass 1.5 x 103 kg. What was the acceleration at the 90 s mark? (A) 0.22 m/s2 (B) 0.33 m/s2 (C) 1.0 m/s2 (D) 9.8 m/s2 (E) 20 m/s2
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Homework (due Friday) Problems
Section D Motion with Constant Acceleration (p.50) #30, 39, 40
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Quiz A stone is thrown straight upward with an initial velocity v0. Sketch graphs: (a) acceleration versus time (b) velocity versus time (c) position versus time.
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