Example Suppose that the position function of a particle moving on a coordinate line is given by...
3
Example • Suppose that the position function of a particle moving on a coordinate line is given by s(t) = 2t 3 -21t 2 +60t+3 Analyze the motion of the particle for t> 0 position 60 42 6 ) ( ) ( ' 2 t t t v t s velocity ) 5 )( 2 ( 6 ) 10 7 ( 6 2 t t t t 42 12 ) ( ) ( ' ) ( ' ' t t a t v t s Acceleration
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Transcript of Example Suppose that the position function of a particle moving on a coordinate line is given by...
Example
• Suppose that the position function of a particle moving on a coordinate line is given by s(t) = 2t3-21t2+60t+3 Analyze the motion of the particle for t>0
position 60426)()(' 2 tttvtsvelocity
)5)(2(6
)107(6 2
tt
tt4212)()(')('' ttatvts
Acceleration
Example
Suppose that the position function of a particle moving on a coordinate line is given by s(t) = 2t3-21t2+60t+3 Analyze the motion of the particle for t>0
Graphically Algebraically Meaning
Pos
ition
Vel
ocity
Acc
eler
atio
n
0360212)( 23 tttts
Never 0 (t>0), always postive
Always on postive side of number line
060426)()( 2 tttvts0)107(6 2 tt0)5)(2(6 tt
0 2 5
+ - +0 0
0<t<2 going pos direction
t=2 turning
2<t<5 going neg. directiont=5 turning
t>5 going pos. direction
t=0 t=2t=5
04212)()( ttatv4212 t 5.3t
+ - - +
0 2 53.5
va - - + +
0<t<2 slowing down
2<t<3.5 speeding up
3.5<t<5 slowing down
5<t speeding up
position 60426)()(' 2 tttvtsvelocity
)5)(2(6
)107(6 2
tt
tt4212)()(')('' ttatvts
Acceleration
Position
t
Direction of motion
0 2 5
+++ --- +++
stop stop
positive direction
negativedirection
positive direction 0 2 5
v(t)+++ --- +++
7/2
a(t)----------- ++++++
slo
win
g
do
wn
spe
ed
ing
up
slo
win
g
do
wn
spe
ed
ing
up
