old 5 answer - oldhomewk 05 NOORANI, ZOHEB Due: Jan 27...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: oldhomewk 05 NOORANI, ZOHEB Due: Jan 27 2008, 4:00 am 1 Question 1, chap 2, sect 7. part 1 of 1 10 points An object is released from rest at time t = 0 and falls through the air, which exerts a resistive force such that the acceleration a of the object is given by a = g b v , where v is the objects speed and b is a constant. If limiting cases for large and small values of t are considered, which of the following is a possible expression for the speed of the object as an explicit function of time? 1. v = g t b t 2 2. v = g ( 1 e bt ) b correct 3. v = ( g e bt ) b 4. v = ( g + a ) t b 5. v = v + g t, v negationslash = 0 Explanation: At time t = 0, the speed of the object is zero, and at time t = , the acceleration is zero, corresponding to a speed v = g b . Check the five choices, and it shows that the only possible answer is v = g ( 1 e bt ) b . Note: The answer can be directly obtained by integration: a = g b v d v dt = g parenleftbigg b v g 1 parenrightbigg integraldisplay v dv b g v 1 = g integraldisplay t dt g b ln parenleftbigg b g v 1 parenrightbiggvextendsingle vextendsingle vextendsingle vextendsingle v = g t vextendsingle vextendsingle vextendsingle vextendsingle t g b bracketleftBig ln parenleftbigg b g v 1 parenrightbigg ln( 1) bracketrightBig = g t ln parenleftbigg 1 b g v parenrightbigg = b t 1 b g v = e b t b g v = 1 e b t v = g b parenleftBig 1 e b t parenrightBig ....
View Full Document

Page1 / 4

old 5 answer - oldhomewk 05 NOORANI, ZOHEB Due: Jan 27...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online