Accelerate to Max velocity, then decelerate to known velocity
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I have an object traveling at a known velocity (Vi). It then accelerates (known A) to a known maximum velocity (Vmax), then decelerates (-A) to another known velocity (Vf). The total distance traveled is also known (Xf-Xi). I'm looking for an equation that will give me total elapsed time (t) when Xi, Xf, Vi, Vmax, Vf, and A are all known quantities. It also needs to take into account that Vmax may not be attained if the (Xf-Xi) is too small.
physics classical-mechanics
asked Jun 10 '16 at 17:45
Jason Lutz
62
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up vote
1
down vote
favorite
I have an object traveling at a known velocity (Vi). It then accelerates (known A) to a known maximum velocity (Vmax), then decelerates (-A) to another known velocity (Vf). The total distance traveled is also known (Xf-Xi). I'm looking for an equation that will give me total elapsed time (t) when Xi, Xf, Vi, Vmax, Vf, and A are all known quantities. It also needs to take into account that Vmax may not be attained if the (Xf-Xi) is too small.
physics classical-mechanics
asked Jun 10 '16 at 17:45
Jason Lutz
62
1
Does it travel any distance at $V_i$ before accelerating? Does it travel any distance after decelerating to $V_f$? If the answer to both questions is No, then you can easily calculate the time as $frac{V_{max}-V_i}{A}+frac{V_{max}-V_f}{A}$. If the answer to both is Yes, then the total time is indeterminate.
– almagest
Jun 10 '16 at 18:00
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
I have an object traveling at a known velocity (Vi). It then accelerates (known A) to a known maximum velocity (Vmax), then decelerates (-A) to another known velocity (Vf). The total distance traveled is also known (Xf-Xi). I'm looking for an equation that will give me total elapsed time (t) when Xi, Xf, Vi, Vmax, Vf, and A are all known quantities. It also needs to take into account that Vmax may not be attained if the (Xf-Xi) is too small.
physics classical-mechanics
asked Jun 10 '16 at 17:45
Jason Lutz
62
I have an object traveling at a known velocity (Vi). It then accelerates (known A) to a known maximum velocity (Vmax), then decelerates (-A) to another known velocity (Vf). The total distance traveled is also known (Xf-Xi). I'm looking for an equation that will give me total elapsed time (t) when Xi, Xf, Vi, Vmax, Vf, and A are all known quantities. It also needs to take into account that Vmax may not be attained if the (Xf-Xi) is too small.
physics classical-mechanics
physics classical-mechanics
asked Jun 10 '16 at 17:45
Jason Lutz
62
asked Jun 10 '16 at 17:45
Jason Lutz
62
asked Jun 10 '16 at 17:45
Jason Lutz
62
asked Jun 10 '16 at 17:45
Jason Lutz
62
asked Jun 10 '16 at 17:45
Jason Lutz
62
62
1
Does it travel any distance at $V_i$ before accelerating? Does it travel any distance after decelerating to $V_f$? If the answer to both questions is No, then you can easily calculate the time as $frac{V_{max}-V_i}{A}+frac{V_{max}-V_f}{A}$. If the answer to both is Yes, then the total time is indeterminate.
– almagest
Jun 10 '16 at 18:00
add a comment |
1
Does it travel any distance at $V_i$ before accelerating? Does it travel any distance after decelerating to $V_f$? If the answer to both questions is No, then you can easily calculate the time as $frac{V_{max}-V_i}{A}+frac{V_{max}-V_f}{A}$. If the answer to both is Yes, then the total time is indeterminate.
– almagest
Jun 10 '16 at 18:00
1
1
Does it travel any distance at $V_i$ before accelerating? Does it travel any distance after decelerating to $V_f$? If the answer to both questions is No, then you can easily calculate the time as $frac{V_{max}-V_i}{A}+frac{V_{max}-V_f}{A}$. If the answer to both is Yes, then the total time is indeterminate.
– almagest
Jun 10 '16 at 18:00
Does it travel any distance at $V_i$ before accelerating? Does it travel any distance after decelerating to $V_f$? If the answer to both questions is No, then you can easily calculate the time as $frac{V_{max}-V_i}{A}+frac{V_{max}-V_f}{A}$. If the answer to both is Yes, then the total time is indeterminate.
– almagest
Jun 10 '16 at 18:00
add a comment |
1 Answer
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The three important formulas in kinematics are
$$ d=v_it + frac12at^2$$
$$a=frac{v_f-v_i}t$$
$$v_f^2 = v_i^2 + 2ad$$
where
$d =$ travelled distance
$v_i =$ initial velocity
$v_f =$ final velocity
$a =$ acceleration
$t =$ elapsed time
Can you proceed?
edited Nov 18 at 3:16
Parcly Taxel
41.1k137199
answered Jun 11 '16 at 20:11
cgiovanardi
724411
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
The three important formulas in kinematics are
$$ d=v_it + frac12at^2$$
$$a=frac{v_f-v_i}t$$
$$v_f^2 = v_i^2 + 2ad$$
where
$d =$ travelled distance
$v_i =$ initial velocity
$v_f =$ final velocity
$a =$ acceleration
$t =$ elapsed time
Can you proceed?
edited Nov 18 at 3:16
Parcly Taxel
41.1k137199
answered Jun 11 '16 at 20:11
cgiovanardi
724411
add a comment |
up vote
0
down vote
The three important formulas in kinematics are
$$ d=v_it + frac12at^2$$
$$a=frac{v_f-v_i}t$$
$$v_f^2 = v_i^2 + 2ad$$
where
$d =$ travelled distance
$v_i =$ initial velocity
$v_f =$ final velocity
$a =$ acceleration
$t =$ elapsed time
Can you proceed?
edited Nov 18 at 3:16
Parcly Taxel
41.1k137199
answered Jun 11 '16 at 20:11
cgiovanardi
724411
add a comment |
up vote
0
down vote
up vote
0
down vote
The three important formulas in kinematics are
$$ d=v_it + frac12at^2$$
$$a=frac{v_f-v_i}t$$
$$v_f^2 = v_i^2 + 2ad$$
where
$d =$ travelled distance
$v_i =$ initial velocity
$v_f =$ final velocity
$a =$ acceleration
$t =$ elapsed time
Can you proceed?
edited Nov 18 at 3:16
Parcly Taxel
41.1k137199
answered Jun 11 '16 at 20:11
cgiovanardi
724411
The three important formulas in kinematics are
$$ d=v_it + frac12at^2$$
$$a=frac{v_f-v_i}t$$
$$v_f^2 = v_i^2 + 2ad$$
where
$d =$ travelled distance
$v_i =$ initial velocity
$v_f =$ final velocity
$a =$ acceleration
$t =$ elapsed time
Can you proceed?
edited Nov 18 at 3:16
Parcly Taxel
41.1k137199
answered Jun 11 '16 at 20:11
cgiovanardi
724411
edited Nov 18 at 3:16
Parcly Taxel
41.1k137199
edited Nov 18 at 3:16
Parcly Taxel
41.1k137199
edited Nov 18 at 3:16
Parcly Taxel
41.1k137199
41.1k137199
answered Jun 11 '16 at 20:11
cgiovanardi
724411
answered Jun 11 '16 at 20:11
cgiovanardi
724411
answered Jun 11 '16 at 20:11
cgiovanardi
724411
724411
add a comment |
add a comment |
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Does it travel any distance at $V_i$ before accelerating? Does it travel any distance after decelerating to $V_f$? If the answer to both questions is No, then you can easily calculate the time as $frac{V_{max}-V_i}{A}+frac{V_{max}-V_f}{A}$. If the answer to both is Yes, then the total time is indeterminate.
– almagest
Jun 10 '16 at 18:00