course PHY 231
7/10 22:23
Reason out the quantities v0, vf, Dv, vAve, a, Ds and Dt: If an object’s initial velocity is 10 cm/s, and it accelerates uniformly through 36 cm in 3 seconds, then what is its final velocity? v_0 = 10cm/s
'ds = 36cm
'dt = 3s
v_avg = (36/3)cm/s = 12cm/s
v_avg = (v_0 + v_f) / 2
v_f = 2v_avg - v_0 = 2*12cm/s - 10cm/s = 14cm/s
'dv = v_f - v_0 = 4cm/s
a = 'dv/'dt = 1.3cm/s^2
Using the equations which govern uniformly accelerated motion determine vf, v0, a, Ds and Dt for an object which accelerates through a distance of 36 cm, ending with velocity 10 cm/s and accelerating at 1.333 cm/s/s.
v_0 = ?
v_f = 10cm/s
v_avg = ?
'ds = 36cm
'dt = ?
'dv = ?
a = 1.333cm/s^2
(v_f - v_0) = 'dv
(v_f + v_0)/2 = v_avg = 'ds*'dt
a = 'dv/'dt
'dt = 'dv/a
v_avg = 'ds*'dv/a = ('ds/a)*(v_f - v_0) = (v_f + v_0)/2
v_avg = 'ds / ('dv/a)
('ds/a)*(v_f - v_0) = (v_f + v_0)/2
(36cm/s)(s^2/1.333cm)*(10cm/s - v_0) = (10cm/s + v_0)/2
(36cm/1.333cm)(s^2/s)*(10cm/s - v_0)*2 = 10cm/s + v_0
27*2s(10cm/s - v_0) = 10cm/s + v_0
54s(10cm/s - v_0) = 10cm/s + v_0
540*cm*(s/s) - 54*v_0cm(s/s) = 10cm/s + v_0cm/s
????I cannot seem to work this problem out. Is the object starting from rest???
Perhaps, but it is not given that the object starts from rest. If it did, you will conclude this based on the given quantities.
You made an error in your symbolic analysis, which is otherwise well done. See my note.
Your corrected analysis will lead you to conclusions which are equivalent to the third and/or fourth equations of uniformtly accelerated motion.
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