Question

The position function of a particle in rectilinear motion is given by s(t) = 2t3 – 21t2 + 60t + 3 for t ≥ 0. Find the position and acceleration of the particle at the instant the when the particle reverses direction. Include units in your answer.

Answer 1

@jim_thompson5910

Answer 2

@ganeshie8 someone plz help

Answer 3

HI!!

Answer 4

it reversed direction when the derivative is zero

Answer 5

find the derivative
set it equal to zero and solve
save that number
find the second derivative
plug that number in

Answer 6

can u please show me the steps written out? :) to double check myself, plus it helps me learn what exact steps to follow

Answer 7

did you find the derivative? it is a polynomial so that part should be easy

Answer 8

yes i will do that right now :)

Answer 9

6t^2-42t+60

Answer 10

s(t) = 6t^2 - 42t + 60

Answer 11

looks reasonable
now set
\[6t^2-42t+60=0\] and solve
a good first step would be to divide all by 6 and solve
\[t^2-7t+6=0\] which fortunately factors

Answer 12

except i made a dumb mistake (blonde) it is
\[t^2-7t+10=0\] which also factors

Answer 13

haha its okay! thanks for the heads up :) so it would be: ( t + 5 ) ( t + 2) = 0

Answer 14

hmm no

Answer 15

\[(t-5)(t-2)=0\] should work better

Answer 16

im sorry! ahah i didn't catch that :P thank u again :)

Answer 17

which is a good thing because your answers need to be positive, and now they are

Answer 18

:) yes

Answer 19

so i get t = 5 and t = 2? :D

Answer 20

and do i plug those into s(t) =2t^3 - 21t^2 + 60t + 3

Answer 21

@ganeshie8 @jim_thompson5910 okay im all caught up to here, can u please help me with the rest of the math?!? :)

Answer 22

@misty1212

Answer 23

@dan815

Answer 24

@Destinymasha

Answer 25

@freckles @iambatman

Answer 26

@unicwaan