Help with an applications of calculus question (1 Viewer)

[tonysoprano]

Hey guys,

A particle moves in a straight line such that its displacement, x cm, after t seconds is given by: x=t^3 - 6t^2 + 9t + 4.
a. When and where does the particle first change direction? (answer is 1second, 8cm)
b. What is the average speed of the particle in the first second?† (need help with b, the answer is 4 cm/s)

Thanks!

 

[VBN2470]

 

[tonysoprano]

Yep, I got it! Thanks

 

[tonysoprano]

Oh holy shit, I just realised how much of a dumb question that was. I'm going to shoot myself now. GG ATAR when I can't do questions like that.

 

[Silly Sausage]

Wouldn't blame you, most teachers who go over this topic in mathematics only go through the calculus based kinematics and expose their students to little or none of the basic stuff (e.g. the physics they teach you in year 10 science). Most teachers just say: velocity equals without differentiating between instantaneous velocity (gradient of displacement curve at a particular time , hence may involve calculus) and average velocity which is just the average velocity over a period of time.
Note the difference between and is the former is used for infinitesimal change (extremely small), whilst the latter is used for relativity large changes.

 

[InteGrand]

Also, since average speed and not velocity was asked for, we should check that the velocity does not change sign in the time interval in question.

Edit: noticed part a) got us to do this.