Question

The position of a particle is given by:
s(t) = -e^(-t) sin(t)
a)find a formula for velocity of a particle
b) is there a time t when the particle changes direction? if so give a particular value of t where this happens.
c) what is the limit of the velocity of the particle as t tends to infinity?

Answer 1

velocity means derivative
take the derivative to get the answer to A

Answer 2

\[v(t) = -e^{-t}\sin(t) +e ^{-t}\cos(t)\]

Answer 3

ok i believe you
set it equal to zero for part B

Answer 4

\[0 =(-\sin(t)+\cos(t)) e ^{-t}\]

Answer 5

let me check your derivative before we go further

Answer 6

check it again i htink it is wrong
brb

Answer 7

okay

Answer 8

not that it will make any difference when we set it equal to zero and solve, but i think the derivaitve is
\[e^{-t}(\sin(t)-\cos(t))\]

Answer 9

in any case you want
\[\sin(t)-\cos(t)=0\\
\sin(t)=\cos(t)\\
t=\frac{\pi}{4}\] etc

Answer 10

oh okay that makes sense

Answer 11

but then how do i get part c? do i just plug in really big numbers?