Optimization problem, minimal speed of point
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What is the minimal speed of a point moving according to this law:$$S(t)=t^3+3t+1$$ $[m], t-[s]$
Will I get the answer by finding the global minimum of this function? Or is it about finding a point where function declines the most? I'm lost
optimization maxima-minima
asked Jan 9 at 18:35
B. CzostekB. Czostek
556
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add a comment |
$begingroup$
What is the minimal speed of a point moving according to this law:$$S(t)=t^3+3t+1$$ $[m], t-[s]$
Will I get the answer by finding the global minimum of this function? Or is it about finding a point where function declines the most? I'm lost
optimization maxima-minima
asked Jan 9 at 18:35
B. CzostekB. Czostek
556
$endgroup$
$begingroup$
What does $S(t)$ represent here? Speed? Position?
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– pwerth
Jan 9 at 18:37
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Does $t$ stand for time?
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– pendermath
Jan 9 at 18:37
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Yes t stands for time in seconds
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– B. Czostek
Jan 9 at 18:38
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Does $S(t)$ represent position?
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– KM101
Jan 9 at 18:46
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Be careful: in general “speed” is not the same thing as “velocity,” although happily in this case the velocity is always positive.
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– amd
Jan 9 at 20:26
add a comment |
$begingroup$
What is the minimal speed of a point moving according to this law:$$S(t)=t^3+3t+1$$ $[m], t-[s]$
Will I get the answer by finding the global minimum of this function? Or is it about finding a point where function declines the most? I'm lost
optimization maxima-minima
asked Jan 9 at 18:35
B. CzostekB. Czostek
556
$endgroup$
What is the minimal speed of a point moving according to this law:$$S(t)=t^3+3t+1$$ $[m], t-[s]$
Will I get the answer by finding the global minimum of this function? Or is it about finding a point where function declines the most? I'm lost
optimization maxima-minima
optimization maxima-minima
asked Jan 9 at 18:35
B. CzostekB. Czostek
556
asked Jan 9 at 18:35
B. CzostekB. Czostek
556
asked Jan 9 at 18:35
B. CzostekB. Czostek
556
asked Jan 9 at 18:35
B. CzostekB. Czostek
556
asked Jan 9 at 18:35
B. CzostekB. Czostek
556
556
$begingroup$
What does $S(t)$ represent here? Speed? Position?
$endgroup$
– pwerth
Jan 9 at 18:37
$begingroup$
Does $t$ stand for time?
$endgroup$
– pendermath
Jan 9 at 18:37
$begingroup$
Yes t stands for time in seconds
$endgroup$
– B. Czostek
Jan 9 at 18:38
$begingroup$
Does $S(t)$ represent position?
$endgroup$
– KM101
Jan 9 at 18:46
$begingroup$
Be careful: in general “speed” is not the same thing as “velocity,” although happily in this case the velocity is always positive.
$endgroup$
– amd
Jan 9 at 20:26
add a comment |
$begingroup$
What does $S(t)$ represent here? Speed? Position?
$endgroup$
– pwerth
Jan 9 at 18:37
$begingroup$
Does $t$ stand for time?
$endgroup$
– pendermath
Jan 9 at 18:37
$begingroup$
Yes t stands for time in seconds
$endgroup$
– B. Czostek
Jan 9 at 18:38
$begingroup$
Does $S(t)$ represent position?
$endgroup$
– KM101
Jan 9 at 18:46
$begingroup$
Be careful: in general “speed” is not the same thing as “velocity,” although happily in this case the velocity is always positive.
$endgroup$
– amd
Jan 9 at 20:26
$begingroup$
What does $S(t)$ represent here? Speed? Position?
$endgroup$
– pwerth
Jan 9 at 18:37
$begingroup$
What does $S(t)$ represent here? Speed? Position?
$endgroup$
– pwerth
Jan 9 at 18:37
$begingroup$
Does $t$ stand for time?
$endgroup$
– pendermath
Jan 9 at 18:37
$begingroup$
Does $t$ stand for time?
$endgroup$
– pendermath
Jan 9 at 18:37
$begingroup$
Yes t stands for time in seconds
$endgroup$
– B. Czostek
Jan 9 at 18:38
$begingroup$
Yes t stands for time in seconds
$endgroup$
– B. Czostek
Jan 9 at 18:38
$begingroup$
Does $S(t)$ represent position?
$endgroup$
– KM101
Jan 9 at 18:46
$begingroup$
Does $S(t)$ represent position?
$endgroup$
– KM101
Jan 9 at 18:46
$begingroup$
Be careful: in general “speed” is not the same thing as “velocity,” although happily in this case the velocity is always positive.
$endgroup$
– amd
Jan 9 at 20:26
$begingroup$
Be careful: in general “speed” is not the same thing as “velocity,” although happily in this case the velocity is always positive.
$endgroup$
– amd
Jan 9 at 20:26
add a comment |
1 Answer
1
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If this is the displacement of the particle, we have:
$$V(t)=S'(t)=3t^2+3$$
Which is minimal where $t=0$ giving a speed of 3.
If this is the speed of the particle, the speed is minimal at $t=0$ giving a speed of 1.
answered Jan 9 at 18:45
Peter ForemanPeter Foreman
2,5441214
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add a comment |
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1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
If this is the displacement of the particle, we have:
$$V(t)=S'(t)=3t^2+3$$
Which is minimal where $t=0$ giving a speed of 3.
If this is the speed of the particle, the speed is minimal at $t=0$ giving a speed of 1.
answered Jan 9 at 18:45
Peter ForemanPeter Foreman
2,5441214
$endgroup$
add a comment |
$begingroup$
If this is the displacement of the particle, we have:
$$V(t)=S'(t)=3t^2+3$$
Which is minimal where $t=0$ giving a speed of 3.
If this is the speed of the particle, the speed is minimal at $t=0$ giving a speed of 1.
answered Jan 9 at 18:45
Peter ForemanPeter Foreman
2,5441214
$endgroup$
add a comment |
$begingroup$
If this is the displacement of the particle, we have:
$$V(t)=S'(t)=3t^2+3$$
Which is minimal where $t=0$ giving a speed of 3.
If this is the speed of the particle, the speed is minimal at $t=0$ giving a speed of 1.
answered Jan 9 at 18:45
Peter ForemanPeter Foreman
2,5441214
$endgroup$
If this is the displacement of the particle, we have:
$$V(t)=S'(t)=3t^2+3$$
Which is minimal where $t=0$ giving a speed of 3.
If this is the speed of the particle, the speed is minimal at $t=0$ giving a speed of 1.
answered Jan 9 at 18:45
Peter ForemanPeter Foreman
2,5441214
answered Jan 9 at 18:45
Peter ForemanPeter Foreman
2,5441214
answered Jan 9 at 18:45
Peter ForemanPeter Foreman
2,5441214
answered Jan 9 at 18:45
Peter ForemanPeter Foreman
2,5441214
2,5441214
add a comment |
add a comment |
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$begingroup$
What does $S(t)$ represent here? Speed? Position?
$endgroup$
– pwerth
Jan 9 at 18:37
$begingroup$
Does $t$ stand for time?
$endgroup$
– pendermath
Jan 9 at 18:37
$begingroup$
Yes t stands for time in seconds
$endgroup$
– B. Czostek
Jan 9 at 18:38
$begingroup$
Does $S(t)$ represent position?
$endgroup$
– KM101
Jan 9 at 18:46
$begingroup$
Be careful: in general “speed” is not the same thing as “velocity,” although happily in this case the velocity is always positive.
$endgroup$
– amd
Jan 9 at 20:26