Question

The function s(t)=t^3/3-6t^2/2+5t+7 describes the position of a particle in motion. When is the particle moving at a constant speed?

Answer 1

Well first you must find the first dervivative of position which is velocity, then the second one which is acceleration and then solve t for when acceleration is 0, if you give mw time I'll do the maths.

Answer 2

just wolfram it

Answer 3

its a word problem

Answer 4

of the first and second derivative i mean

Answer 5

and i have the derivatives but i thought i had to do what ivancsc1996 suggested but for when the particle is resting

Answer 6

\[\frac{ d }{ dt }s=t ^{2}-6t+5=v\]\[\frac{ d }{ dt }v=2t-6=a \rightarrow a=0 \rightarrow t=3\]The particle is moving at constant speed at t=3s.

Answer 7

so what would i do for when the particle is resting

Answer 8

When the particle is resting is when v=0\[v=t ^{2}-6t+5 \rightarrow v=0 \rightarrow t=5,1\]The particle is resting at 5s and 1s

Answer 9

ok thank you

Answer 10

Well, that's as much as eleventh grade highschool physics can give. I am sorry if I am wrong.

Answer 11

this is actually for an AP Calc class but my teachers isnt the best