The Notion of DerivingDeriving an equation (or a statement) is more than just asserting it. It'sshowing how it must be true (and anything contrary must be false).One doesn't understand the material as long as one is limited tomemorizing statements or equations, without being able to connectthem.As a further, practical thing, understanding the connection makes it lesslikely that one would use an equation when it doesn't apply. Inparticular, one would avoid the "equations of constant acceleration"anytime one had non-constant acceleration.In this assignment, I assign you to derive the "equations of constantacceleration" -- all but one that I will derive. We will use 0, w, and a,satisfying these definitions:dwdeanda =dtW =dtand one special case: a is constant. (You should spot the false stepwhen a is non-constant.) w and 0 are functions of time: w(t) and 0(t).ωο- ω(0), and θ0-θ(0).My Example: derive w2 - wo? = 2a(0-0).dwdw dedwa =dtde dtdeMultiply by dt and integrate:Sadow dw = w?d0 = a0 + C =w?2a0 + 2CSubstitute the initial (t=0) quantities, and subtract. The constant ofintegration vanishes.w3 = 2a0 + 2Cw? – w = 2a(0 – 0o)The e integration fails if a is non-constant. There is also a type ofsituation where the step before the integration fails, involving w. Question 2: derive 0 = 1/2at² + wot+ 0o-You may use prior derived results.

Name: The Notion of DerivingDeriving an equation (or a statement) is more t
Uploaded: 2024-03-05T11:56:34.000Z
Channel: Bartleby
Description: The Notion of DerivingDeriving an equation (or a statement) is more than just asserting it. It'sshowing how it must be true (and anything contrary must be false).One doesn't understand the material as long as one is limited tomemorizing statements o