02prob_11

# 02prob_11 - Assigment#2 Page 1 of 4 UC Davis Physics 9A...

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Unformatted text preview: Assigment #2, 4/8/11 Page 1 of 4 UC Davis Physics 9A Assignment #2 Cole [2.31]  a)   a=dv/dt õ  The instantaneous acceleration is the slope of the  v-t  graph.   a(t=3) =  0,   a(t=7)   =  (45 - 20)(m/s)/(9 - 5)(s)  =  6.25 m/s 2 ,   a(t=11) =  (0 - 45)/(13 - 9)  =  - 11.25 m/s 2 b)  The displacement is   Îx = ¡ v dt = area under v-t graph.   Îx 1  =  (20 m/s)(5 s)  = 100 m Îx 2   =  (20 m/s)(9 s) +  1 2 (25 m/s)(4s)  = 230 m.   Îx 3   =  230 m +  1 2 (45 m/s)(13 s - 9 s)  =  320 m. [2.40]  We are given information on the speed and distance but not the time.  We can use the the  formula with the time eliminated.   v 2  = vø 2  + 2aÎx  õ    v = 0.8 m/s ( ) 2 + 2 1.6 m/s 2 ( ) 5 m ( )   =  4.1 m/s [2.75]  a)  The acceleration depends on time so we must integrate:   dv v v ∫ = a dt t ∫ = − 2 + 3 t ( ) dt t ∫    õ  v = v − 2 t + 3 2 t 2 , and integrate again to find position:  dx x x ∫ = v − 2 t + 3 t 2 2 ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ dt t ∫   x − x = v t − t 2 + t 3 2   õ  At  t = 4 s,  x = xø   õ   = v − 4 + 4 2 2   õ   vø =  - 4.0 m/s.    b)  v = v − 2 t + 3 2 t 2   õ  v = − 4 − 8 + 3 2 4 2 = +12.0 m/s. [2.80]  Set the origin at the bottom of the top of the window with the positive direction down.   Then use  x = x + v t + 1 2 at 2   where  x ø  =  0.  The flower pot falls through a height  h,  at the top  of the bottom window:   h = 1 2 gt 2 .  There are two unknowns so we need another equation.  At the  bottom of the window:    h + 1.9 m = 1 2 g t + 0.42 s ( ) 2   Plugging the first into the second equation  and Solving for  t: 1 2 gt 2 + 1.9 m = 1 2 g t 2 + 2 0.42 s ( ) t + 0.42 s ( ) 2 ( )   õ   t = 1.9 m 9.8m/s 2 ( ) 0.42 s ( ) − 0.42 s 2  =  0.25 s.  õ   h = 1 2 9.8 m/s 2 ( ) 0.25 ( ) 2  = 0.31 m. [2.90]  a)  First find the time the student takes to hit            b) the ground. Position the origin at the bottom with the positive  direction upwards.  Then,  y  = yø + vøt +   1 2   at  2    where   yø  = 180 m,  vø  = 0, and  a =  -g   so that   y   =  yø -  1 2 gt 2 .   Solve for  t :     t = 2 y − y ( ) g = 2 180  m ( ) 9.8  m/s 2    =  6.06 s.  Superman has 5 seconds less than this    =  6....
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02prob_11 - Assigment#2 Page 1 of 4 UC Davis Physics 9A...

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