Here's part of problem from a college physics text:

A time-dependent force F = (8.00 i - 4.00 t j) N (where t is in seconds) is applied to a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s?

Here's one way to solve the problem using Reduce:

{
  vx == Integrate[Fx/m, {t, 0, t}],
  vy == Integrate[c*t/m, {t, 0, t}],
  speed^2 == vx^2 + vy^2,
  c != 0, speed != 0, Fx != 0
  };
Reduce[%, {t, vx, vy}];
% /. {speed -> 15, Fx -> 8, c -> -4, m -> 2}

The output is:

(t == -5 I || t == 5 I || t == -3 || t == 3) && vx == 4 t && 
 vy == -((t vx)/4)

The answer given in the book is t = 3.

In the set of equations passed to Reduce, the Fx/m comes from Fx = m * ax and c*t/m comes from c*t = m * ay. Instead of doing that manual substitution, I'd like to pass those equations to Reduce and have it do the right thing. I.e. something like:

{
  Fx == m * ax,
  c*t == m * ay,
  vx == Integrate[ax, {t, 0, t}],
  vy == Integrate[ay, {t, 0, t}],
  speed^2 == vx^2 + vy^2,
  c != 0, speed != 0, Fx != 0
  };
Reduce[%, {t, vx, vy}];
% /. {speed -> 15, Fx -> 8, c -> -4, m -> 2}

Of course, that doesn't work because Integrate doesn't know that ax and ay are in terms of t.

Any suggestions on how to make something like this work?

Here's part of problem from a college physics text:

A time-dependent force F = (8.00 i - 4.00 t j) N (where t is in seconds) is applied to a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s?

Here's one way to solve the problem using Reduce:

{
  vx == Integrate[Fx/m, {t, 0, t}],
  vy == Integrate[c*t/m, {t, 0, t}],
  speed^2 == vx^2 + vy^2,
  c != 0, speed != 0, Fx != 0
  };
Reduce[%, {t, vx, vy}];
% /. {speed -> 15, Fx -> 8, c -> -4, m -> 2}

The output is:

(t == -5 I || t == 5 I || t == -3 || t == 3) && vx == 4 t && 
 vy == -((t vx)/4)

The answer given in the book is t = 3.

In the set of equations passed to Reduce, the Fx/m comes from Fx = m * ax and c*t/m comes from c*t = m * ay. Instead of doing that manual substitution, I'd like to pass those equations to Reduce and have it do the right thing. I.e. something like:

{
  Fx == m * ax,
  c*t == m * ay,
  vx == Integrate[ax, {t, 0, t}],
  vy == Integrate[ay, {t, 0, t}],
  speed^2 == vx^2 + vy^2,
  c != 0, speed != 0, Fx != 0
  };
Reduce[%, {t, vx, vy}];
% /. {speed -> 15, Fx -> 8, c -> -4, m -> 2}

Of course, that doesn't work because Integrate doesn't know that ax and ay are in terms of t.

Any suggestions on how to make something like this work?

Here's part of problem from a college physics text:

A time-dependent force F = (8.00 i - 4.00 t j) N (where t is in seconds) is applied to a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s?

Here's one way to solve the problem using Reduce:

{
  vx == Integrate[Fx/m, {t, 0, t}],
  vy == Integrate[c*t/m, {t, 0, t}],
  speed^2 == vx^2 + vy^2,
  c != 0, speed != 0, Fx != 0
  };
Reduce[%, {t, vx, vy}];
% /. {speed -> 15, Fx -> 8, c -> -4, m -> 2}

The output is:

(t == -5 I || t == 5 I || t == -3 || t == 3) && vx == 4 t && 
 vy == -((t vx)/4)

The answer given in the book is t = 3.

In the set of equations passed to Reduce, the Fx/m comes from Fx = m * ax and c*t/m comes from c*t = m * ay. Instead of doing that manual substitution, I'd like to pass those equations to Reduce and have it do the right thing. I.e. something like:

{
  Fx = m * ax,
  c*t = m * ay,
  vx == Integrate[ax, {t, 0, t}],
  vy == Integrate[ay, {t, 0, t}],
  speed^2 == vx^2 + vy^2,
  c != 0, speed != 0, Fx != 0
  };
Reduce[%, {t, vx, vy}];
% /. {speed -> 15, Fx -> 8, c -> -4, m -> 2}

Of course, that doesn't work because Integrate doesn't know that ax and ay are in terms of t.

Any suggestions on how to make something like this work?

Here's part of problem from a college physics text:

A time-dependent force F = (8.00 i - 4.00 t j) N (where t is in seconds) is applied to a 2.00-kg object initially at rest. (a) At what time will the object be moving with a speed of 15.0 m/s?

Here's one way to solve the problem using Reduce:

{
  vx == Integrate[Fx/m, {t, 0, t}],
  vy == Integrate[c*t/m, {t, 0, t}],
  speed^2 == vx^2 + vy^2,
  c != 0, speed != 0, Fx != 0
  };
Reduce[%, {t, vx, vy}];
% /. {speed -> 15, Fx -> 8, c -> -4, m -> 2}

The output is:

(t == -5 I || t == 5 I || t == -3 || t == 3) && vx == 4 t && 
 vy == -((t vx)/4)

The answer given in the book is t = 3.

In the set of equations passed to Reduce, the Fx/m comes from Fx = m * ax and c*t/m comes from c*t = m * ay. Instead of doing that manual substitution, I'd like to pass those equations to Reduce and have it do the right thing. I.e. something like:

{
  Fx == m * ax,
  c*t == m * ay,
  vx == Integrate[ax, {t, 0, t}],
  vy == Integrate[ay, {t, 0, t}],
  speed^2 == vx^2 + vy^2,
  c != 0, speed != 0, Fx != 0
  };
Reduce[%, {t, vx, vy}];
% /. {speed -> 15, Fx -> 8, c -> -4, m -> 2}

Of course, that doesn't work because Integrate doesn't know that ax and ay are in terms of t.

Any suggestions on how to make something like this work?