Question

Calculus. s=(t^3)/3 -6t^2 +50t
with what value of t does the object have a minimum velocity.

Answer 1

ive worked the velocity equation out by differentiating the equation, and have got t^2 -12t +50

Answer 2

so then t^2 -12t +50 =0

Answer 3

i cant factorise this to find the points by which the gradient = 0

Answer 4

then use the quadratic formula

Answer 5

in case you forgot\[ax^2+bx+c=0\implies x={-b\pm\sqrt{b^2-4ac}\over2a}\]

Answer 6

ah ok, havent used that in ages, cheers mate

Answer 7

i need to get 6

Answer 8

and using this formula i just get a mathematics error

Answer 9

oh I didn't read your Q carefully enough, my bad...

Answer 10

no worries mate

Answer 11

you are given a function for position, and you want to minimize velocity
velocity is the first derivative of position
to find max/mins for the velocity function you have to take the derivative again, and set \(that\) equal to zero

Answer 12

why do you take the second derivative? the second derivative is the derivative of a quadratic

Answer 13

thus being linear

Answer 14

to find the max/mins of any function take the derivative and set it to zero

Answer 15

could you please explain this to me, the second derivative is meant to give a point of inflection or tell you the nature of a turning point, so says my maths teacher

Answer 16

but when i set the equation to 0 i get an equation that is unfactorable

Answer 17

you are given position, derivative of position is velocity
to find the max/min of the velocity function though you must set the derivative of *that function* equal to zero
yes setting the second derivative of the position function equal to zero will also tell you a point of inflection, but for the *position* function, not the velocity one

you already have the velocity function, so take the derivative of that and set it to zero

Answer 18

ah yes i see now, so taking the derivative of the velocity function will give you the maximum/minimum of it. But since the velocity function is a parabola it will only give you a max or min

Answer 19

Cheers for that mate ;)

Answer 20

solving s(t)=0 tells you when position is zer
solving s'(t)=0 tells you the max/mins of the position and when the velocity is zero
we don't want that, we want to know the max/mins of the velocity function so solve
s''(t)=0

you're welcome (from across the pond I assume)!

Answer 21

haha yes, guess you can tell where then haha.

Answer 22

judging by the term im assuming your british?

Answer 23

no, but my stepfather is so I'm quite familiar with British English
I'm a US citizen living in Mexico

Answer 24

Ah, interesting. Well Aussie here mate, haha, cheers for the help. Not familiar with the time zones, but i believe its day time over there, so have a good day mate.

Answer 25

ah, then you're more than the "pond" away :P
see ya around!