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review derivation: equations of motion in 2D (calculus)

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Index Inference Rule Input latex Feeds latex Output latex step validity dimension check unit check notes
1 declare initial expr
  1. 3169580383; locally 6758737:
    \(\vec{a} = \frac{d\vec{v}}{dt}\)
    \(pdg_{2423} = \frac{d}{d pdg_{1467}} pdg_{6373}\)
no validation is available for declarations 3169580383:
3169580383:
3 substitute LHS of expr 1 into expr 2
  1. 3169580383; locally 6758737:
    \(\vec{a} = \frac{d\vec{v}}{dt}\)
    \(pdg_{2423} = \frac{d}{d pdg_{1467}} pdg_{6373}\)
  2. 8602512487; locally 4862823:
    \(\vec{a} = a_x \hat{x} + a_y \hat{y}\)
    \(pdg_{2423} = pdg_{1700} pdg_{7055} + pdg_{7159} pdg_{8339}\)
  1. 4158986868; locally 4755350:
    \(a_x \hat{x} + a_y \hat{y} = \frac{d\vec{v}}{dt}\)
    \(pdg_{1467}\)
Nothing to split 3169580383:
8602512487:
4158986868:
3169580383:
8602512487:
4158986868:
5 substitute LHS of expr 1 into expr 2
  1. 5349866551; locally 5359560:
    \(\vec{v} = v_x \hat{x} + v_y \hat{y}\)
    \(pdg_{6373} = pdg_{1700} pdg_{9107} + pdg_{5505} pdg_{8339}\)
  2. 4158986868; locally 4755350:
    \(a_x \hat{x} + a_y \hat{y} = \frac{d\vec{v}}{dt}\)
    \(pdg_{1467}\)
  1. 7729413831; locally 4904941:
    \(a_x \hat{x} + a_y \hat{y} = \frac{d}{dt} \left(v_x \hat{x} + v_y \hat{y} \right)\)
    \(pdg_{1700} pdg_{7055} + pdg_{7159} pdg_{8339} = \frac{\partial}{\partial pdg_{1467}} \left(pdg_{1700} pdg_{9107} + pdg_{5505} pdg_{8339}\right)\)
Nothing to split 5349866551:
4158986868:
7729413831:
5349866551:
4158986868:
7729413831:
6 separate two vector components
  1. 7729413831; locally 4904941:
    \(a_x \hat{x} + a_y \hat{y} = \frac{d}{dt} \left(v_x \hat{x} + v_y \hat{y} \right)\)
    \(pdg_{1700} pdg_{7055} + pdg_{7159} pdg_{8339} = \frac{\partial}{\partial pdg_{1467}} \left(pdg_{1700} pdg_{9107} + pdg_{5505} pdg_{8339}\right)\)
  1. 1819663717; locally 5765841:
    \(a_x = \frac{d}{dt} v_x\)
    \(pdg_{7159} = \frac{d}{d pdg_{1467}} pdg_{5505}\)
  2. 8228733125; locally 2080932:
    \(a_y = \frac{d}{dt} v_y\)
    \(pdg_{7055} = \frac{d}{d pdg_{1467}} pdg_{9107}\)
no check performed 7729413831:
1819663717:
8228733125:
7729413831:
1819663717:
8228733125:
7 declare assumption
  1. 9707028061; locally 2060958:
    \(a_x = 0\)
    \(pdg_{7159} = 0\)
no validation is available for declarations 9707028061:
9707028061:
define the orientation of the coordinate system with respect to the gravitational acceleration such that x axis is perpendicular to gravity
8 declare assumption
  1. 2741489181; locally 1439312:
    \(a_y = -g\)
    \(pdg_{7055} = - pdg_{1649}\)
no validation is available for declarations 2741489181:
2741489181:
define the orientation of the coordinate system with respect to the gravitational acceleration such that y axis is parallel to gravity
9 assume N dimensions
  1. 3270039798:
    \(2\)
    \(2\)
  1. 8602512487; locally 4862823:
    \(\vec{a} = a_x \hat{x} + a_y \hat{y}\)
    \(pdg_{2423} = pdg_{1700} pdg_{7055} + pdg_{7159} pdg_{8339}\)
no validation is available for assumptions 8602512487:
8602512487:
10 assume N dimensions
  1. 8880467139:
    \(2\)
    \(2\)
  1. 5349866551; locally 5359560:
    \(\vec{v} = v_x \hat{x} + v_y \hat{y}\)
    \(pdg_{6373} = pdg_{1700} pdg_{9107} + pdg_{5505} pdg_{8339}\)
no validation is available for assumptions 5349866551:
5349866551:
11 substitute LHS of expr 1 into expr 2
  1. 9707028061; locally 2060958:
    \(a_x = 0\)
    \(pdg_{7159} = 0\)
  2. 1819663717; locally 5765841:
    \(a_x = \frac{d}{dt} v_x\)
    \(pdg_{7159} = \frac{d}{d pdg_{1467}} pdg_{5505}\)
  1. 8750379055; locally 8742281:
    \(0 = \frac{d}{dt} v_x\)
    \(0 = \frac{d}{d pdg_{1467}} pdg_{5505}\)
valid 9707028061:
1819663717:
8750379055:
9707028061:
1819663717:
8750379055:
12 substitute LHS of expr 1 into expr 2
  1. 2741489181; locally 1439312:
    \(a_y = -g\)
    \(pdg_{7055} = - pdg_{1649}\)
  2. 8228733125; locally 2080932:
    \(a_y = \frac{d}{dt} v_y\)
    \(pdg_{7055} = \frac{d}{d pdg_{1467}} pdg_{9107}\)
  1. 1977955751; locally 3939933:
    \(-g = \frac{d}{dt} v_y\)
    \(- pdg_{1649} = \frac{d}{d pdg_{1467}} pdg_{9107}\)
valid 2741489181:
8228733125:
1977955751:
2741489181:
8228733125:
1977955751:
13 multiply both sides by
  1. 1977955751; locally 3939933:
    \(-g = \frac{d}{dt} v_y\)
    \(- pdg_{1649} = \frac{d}{d pdg_{1467}} pdg_{9107}\)
  1. 6672141531:
    \(dt\)
    \(pdg_{4711}\)
  1. 1702349646; locally 4777195:
    \(-g dt = d v_y\)
    \(- dt pdg_{1649} = pdg_{5674}\)
LHS diff is pdg1649*(dt - pdg4711) RHS diff is -pdg5674 1977955751:
1702349646:
1977955751:
1702349646:
14 indefinite integration
  1. 1702349646; locally 4777195:
    \(-g dt = d v_y\)
    \(- dt pdg_{1649} = pdg_{5674}\)
  1. 8584698994; locally 3366698:
    \(-g \int dt = \int d v_y\)
    \(- dt g = pdg_{5674}\)
no check performed 1702349646:
8584698994:
1702349646:
8584698994:
15 simplify
  1. 8584698994; locally 3366698:
    \(-g \int dt = \int d v_y\)
    \(- dt g = pdg_{5674}\)
  1. 9973952056; locally 1321587:
    \(-g t = v_y - v_{0, y}\)
    \(- pdg_{1467} pdg_{1649} = - pdg_{5153} + pdg_{9431}\)
LHS diff is -dt*g + pdg1467*pdg1649 RHS diff is pdg5153 + pdg5674 - pdg9431 8584698994:
9973952056:
8584698994:
9973952056:
16 add X to both sides
  1. 9973952056; locally 1321587:
    \(-g t = v_y - v_{0, y}\)
    \(- pdg_{1467} pdg_{1649} = - pdg_{5153} + pdg_{9431}\)
  1. 4167526462:
    \(v_{0, y}\)
    \(pdg_{9431}\)
  1. 6572039835; locally 2682139:
    \(-g t + v_{0, y} = v_y\)
    \(- pdg_{1467} pdg_{1649} + pdg_{9431} = pdg_{9107}\)
LHS diff is 0 RHS diff is -pdg5153 - pdg9107 + 2*pdg9431 9973952056:
6572039835:
9973952056:
6572039835:
17 declare initial expr
  1. 7252338326; locally 3936380:
    \(v_y = \frac{dy}{dt}\)
    \(pdg_{9107} = \frac{d}{d pdg_{1467}} pdg_{5647}\)
no validation is available for declarations 7252338326:
7252338326:
18 substitute LHS of expr 1 into expr 2
  1. 7252338326; locally 3936380:
    \(v_y = \frac{dy}{dt}\)
    \(pdg_{9107} = \frac{d}{d pdg_{1467}} pdg_{5647}\)
  2. 6572039835; locally 2682139:
    \(-g t + v_{0, y} = v_y\)
    \(- pdg_{1467} pdg_{1649} + pdg_{9431} = pdg_{9107}\)
  1. 6204539227; locally 5010170:
    \(-g t + v_{0, y} = \frac{dy}{dt}\)
    \(- g pdg_{1467} + pdg_{9431} = \frac{d}{d pdg_{1467}} pdg_{5647}\)
LHS diff is pdg1467*(g - pdg1649) RHS diff is 0 7252338326:
6572039835:
6204539227:
7252338326:
6572039835:
6204539227:
19 multiply both sides by
  1. 6204539227; locally 5010170:
    \(-g t + v_{0, y} = \frac{dy}{dt}\)
    \(- g pdg_{1467} + pdg_{9431} = \frac{d}{d pdg_{1467}} pdg_{5647}\)
  1. 1614343171:
    \(dt\)
    \(pdg_{4711}\)
  1. 8145337879; locally 5577963:
    \(-g t dt + v_{0, y} dt = dy\)
    \(- pdg_{1467} pdg_{1649} pdg_{4711} + pdg_{4711} pdg_{9431} = pdg_{5842}\)
LHS diff is pdg1467*pdg4711*(-g + pdg1649) RHS diff is -pdg5842 6204539227:
8145337879:
6204539227:
8145337879:
20 indefinite integration
  1. 8145337879; locally 5577963:
    \(-g t dt + v_{0, y} dt = dy\)
    \(- pdg_{1467} pdg_{1649} pdg_{4711} + pdg_{4711} pdg_{9431} = pdg_{5842}\)
  1. 8808860551; locally 8020644:
    \(-g \int t dt + v_{0, y} \int dt = \int dy\)
    \(- pdg_{1649} \int pdg_{1467}\, dpdg_{1467} + pdg_{9431} \int 1\, dpdg_{1467} = \int 1\, dpdg_{5647}\)
no check performed 8145337879:
8808860551:
8145337879:
8808860551:
21 simplify
  1. 8808860551; locally 8020644:
    \(-g \int t dt + v_{0, y} \int dt = \int dy\)
    \(- pdg_{1649} \int pdg_{1467}\, dpdg_{1467} + pdg_{9431} \int 1\, dpdg_{1467} = \int 1\, dpdg_{5647}\)
  1. 2858549874; locally 8638087:
    \(- \frac{1}{2} g t^2 + v_{0, y} t = y - y_0\)
    \(- \frac{pdg_{1467}^{2} pdg_{1649}}{2} + pdg_{1467} pdg_{9431} = - pdg_{1469} + pdg_{5647}\)
LHS diff is 0 RHS diff is pdg1469 8808860551:
2858549874:
8808860551:
2858549874:
22 add X to both sides
  1. 2858549874; locally 8638087:
    \(- \frac{1}{2} g t^2 + v_{0, y} t = y - y_0\)
    \(- \frac{pdg_{1467}^{2} pdg_{1649}}{2} + pdg_{1467} pdg_{9431} = - pdg_{1469} + pdg_{5647}\)
  1. 6098638221:
    \(y_0\)
    \(pdg_{1469}\)
  1. 2461349007; locally 7541692:
    \(- \frac{1}{2} g t^2 + v_{0, y} t + y_0 = y\)
    \(- \frac{pdg_{1467}^{2} pdg_{1649}}{2} + pdg_{1467} pdg_{9431} + pdg_{1469} = pdg_{5647}\)
valid 2858549874:
2461349007:
2858549874:
2461349007:
23 multiply both sides by
  1. 8750379055; locally 8742281:
    \(0 = \frac{d}{dt} v_x\)
    \(0 = \frac{d}{d pdg_{1467}} pdg_{5505}\)
  1. 8717193282:
    \(dt\)
    \(pdg_{4711}\)
  1. 1166310428; locally 5239397:
    \(0 dt = d v_x\)
    \(0 = pdg_{5005}\)
LHS diff is 0 RHS diff is -pdg5005 8750379055:
1166310428:
8750379055:
1166310428:
24 indefinite integration
  1. 1166310428; locally 5239397:
    \(0 dt = d v_x\)
    \(0 = pdg_{5005}\)
  1. 2366691988; locally 3137944:
    \(\int 0 dt = \int d v_x\)
    \(\int 0\, dpdg_{1467} = \int 1\, dpdg_{5005}\)
no check performed 1166310428:
2366691988:
1166310428:
2366691988:
25 simplify
  1. 2366691988; locally 3137944:
    \(\int 0 dt = \int d v_x\)
    \(\int 0\, dpdg_{1467} = \int 1\, dpdg_{5005}\)
  1. 1676472948; locally 9737190:
    \(0 = v_x - v_{0, x}\)
    \(0 = - pdg_{2958} + pdg_{5505}\)
LHS diff is 0 RHS diff is pdg2958 + pdg5005 - pdg5505 2366691988:
1676472948:
2366691988:
1676472948:
26 add X to both sides
  1. 1676472948; locally 9737190:
    \(0 = v_x - v_{0, x}\)
    \(0 = - pdg_{2958} + pdg_{5505}\)
  1. 1439089569:
    \(v_{0, x}\)
    \(pdg_{2958}\)
  1. 6134836751; locally 8435615:
    \(v_{0, x} = v_x\)
    \(pdg_{2958} = pdg_{5505}\)
valid 1676472948:
6134836751:
1676472948:
6134836751:
27 declare initial expr
  1. 8460820419; locally 4895553:
    \(v_x = \frac{dx}{dt}\)
    \(pdg_{5505} = \frac{d}{d pdg_{1467}} pdg_{9199}\)
no validation is available for declarations 8460820419:
8460820419:
28 substitute LHS of expr 1 into expr 2
  1. 6134836751; locally 8435615:
    \(v_{0, x} = v_x\)
    \(pdg_{2958} = pdg_{5505}\)
  2. 8460820419; locally 4895553:
    \(v_x = \frac{dx}{dt}\)
    \(pdg_{5505} = \frac{d}{d pdg_{1467}} pdg_{9199}\)
  1. 7455581657; locally 5123314:
    \(v_{0, x} = \frac{dx}{dt}\)
    \(pdg_{2958} = \frac{d}{d pdg_{1467}} pdg_{9199}\)
LHS diff is -pdg2958 + pdg5505 RHS diff is 0 6134836751:
8460820419:
7455581657:
6134836751:
8460820419:
7455581657:
29 multiply both sides by
  1. 7455581657; locally 5123314:
    \(v_{0, x} = \frac{dx}{dt}\)
    \(pdg_{2958} = \frac{d}{d pdg_{1467}} pdg_{9199}\)
  1. 8607458157:
    \(dt\)
    \(pdg_{4711}\)
  1. 1963253044; locally 8062944:
    \(v_{0, x} dt = dx\)
    \(pdg_{2958} pdg_{4711} = pdg_{9199}\)
LHS diff is 0 RHS diff is -pdg9199 7455581657:
1963253044:
7455581657:
1963253044:
30 indefinite integration
  1. 1963253044; locally 8062944:
    \(v_{0, x} dt = dx\)
    \(pdg_{2958} pdg_{4711} = pdg_{9199}\)
  1. 3676159007; locally 2732393:
    \(v_{0, x} \int dt = \int dx\)
    \(pdg_{2958} \int 1\, dpdg_{1467} = \int 1\, dpdg_{1464}\)
no check performed 1963253044:
3676159007:
1963253044:
3676159007:
31 simplify
  1. 3676159007; locally 2732393:
    \(v_{0, x} \int dt = \int dx\)
    \(pdg_{2958} \int 1\, dpdg_{1467} = \int 1\, dpdg_{1464}\)
  1. 9882526611; locally 2740672:
    \(v_{0, x} t = x - x_0\)
    \(pdg_{1467} pdg_{2958} = - pdg_{1572} + pdg_{4037}\)
LHS diff is 0 RHS diff is pdg1464 + pdg1572 - pdg4037 3676159007:
9882526611:
3676159007:
9882526611:
32 add X to both sides
  1. 9882526611; locally 2740672:
    \(v_{0, x} t = x - x_0\)
    \(pdg_{1467} pdg_{2958} = - pdg_{1572} + pdg_{4037}\)
  1. 3182907803:
    \(x_0\)
    \(pdg_{1572}\)
  1. 8486706976; locally 6277762:
    \(v_{0, x} t + x_0 = x\)
    \(pdg_{1467} pdg_{2958} + pdg_{1572} = pdg_{4037}\)
valid 9882526611:
8486706976:
9882526611:
8486706976:
33 swap LHS with RHS
  1. 8486706976; locally 6277762:
    \(v_{0, x} t + x_0 = x\)
    \(pdg_{1467} pdg_{2958} + pdg_{1572} = pdg_{4037}\)
  1. 1306360899; locally 3011802:
    \(x = v_{0, x} t + x_0\)
    \(pdg_{4037} = pdg_{1467} pdg_{2958} + pdg_{1572}\)
valid 8486706976:
1306360899:
8486706976:
1306360899:
34 assume N dimensions
  1. 7049769409:
    \(2\)
    \(2\)
  1. 9341391925; locally 1381925:
    \(\vec{v}_0 = v_{0, x} \hat{x} + v_{0, y} \hat{y}\)
    \(pdg_{6091} = pdg_{1700} pdg_{9431} + pdg_{2958} pdg_{8339}\)
no validation is available for assumptions 9341391925:
9341391925:
35 separate vector into two trigonometric ratios
  1. 9341391925; locally 1381925:
    \(\vec{v}_0 = v_{0, x} \hat{x} + v_{0, y} \hat{y}\)
    \(pdg_{6091} = pdg_{1700} pdg_{9431} + pdg_{2958} pdg_{8339}\)
  1. 6410818363:
    \(\theta\)
    \(pdg_{1575}\)
  1. 7391837535; locally 5523081:
    \(\cos(\theta) = \frac{v_{0, x}}{v_0}\)
    \(\cos{\left(pdg_{1575} \right)} = \frac{pdg_{5153}}{pdg_{2958}}\)
  2. 7376526845; locally 2378061:
    \(\sin(\theta) = \frac{v_{0, y}}{v_0}\)
    \(\sin{\left(pdg_{1575} \right)} = \frac{pdg_{5153}}{pdg_{9431}}\)
no check performed 9341391925:
7391837535:
7376526845:
9341391925:
7391837535:
7376526845:
36 multiply both sides by
  1. 7391837535; locally 5523081:
    \(\cos(\theta) = \frac{v_{0, x}}{v_0}\)
    \(\cos{\left(pdg_{1575} \right)} = \frac{pdg_{5153}}{pdg_{2958}}\)
  1. 5868731041:
    \(v_0\)
    \(pdg_{5153}\)
  1. 6083821265; locally 6010171:
    \(v_0 \cos(\theta) = v_{0, x}\)
    \(pdg_{5153} \cos{\left(pdg_{1575} \right)} = pdg_{2958}\)
LHS diff is 0 RHS diff is -pdg2958 + pdg5153**2/pdg2958 7391837535:
6083821265:
7391837535:
6083821265:
37 substitute LHS of expr 1 into expr 2
  1. 6083821265; locally 6010171:
    \(v_0 \cos(\theta) = v_{0, x}\)
    \(pdg_{5153} \cos{\left(pdg_{1575} \right)} = pdg_{2958}\)
  2. 1306360899; locally 3011802:
    \(x = v_{0, x} t + x_0\)
    \(pdg_{4037} = pdg_{1467} pdg_{2958} + pdg_{1572}\)
  1. 5438722682; locally 6795282:
    \(x = v_0 t \cos(\theta) + x_0\)
    \(pdg_{4037} = pdg_{1467} pdg_{5153} \cos{\left(pdg_{1575} \right)} + pdg_{1572}\)
LHS diff is 0 RHS diff is pdg1467*(pdg2958 - pdg5153*cos(pdg1575)) 6083821265:
1306360899:
5438722682:
6083821265:
1306360899:
5438722682:
38 declare final expr
  1. 5438722682; locally 6795282:
    \(x = v_0 t \cos(\theta) + x_0\)
    \(pdg_{4037} = pdg_{1467} pdg_{5153} \cos{\left(pdg_{1575} \right)} + pdg_{1572}\)
no validation is available for declarations 5438722682:
5438722682:
39 multiply both sides by
  1. 7376526845; locally 2378061:
    \(\sin(\theta) = \frac{v_{0, y}}{v_0}\)
    \(\sin{\left(pdg_{1575} \right)} = \frac{pdg_{5153}}{pdg_{9431}}\)
  1. 5620558729:
    \(v_0\)
    \(pdg_{5153}\)
  1. 8949329361; locally 3041148:
    \(v_0 \sin(\theta) = v_{0, y}\)
    \(pdg_{5153} \sin{\left(pdg_{1575} \right)} = pdg_{9431}\)
LHS diff is 0 RHS diff is pdg5153**2/pdg9431 - pdg9431 7376526845:
8949329361:
7376526845:
8949329361:
40 swap LHS with RHS
  1. 2461349007; locally 7541692:
    \(- \frac{1}{2} g t^2 + v_{0, y} t + y_0 = y\)
    \(- \frac{pdg_{1467}^{2} pdg_{1649}}{2} + pdg_{1467} pdg_{9431} + pdg_{1469} = pdg_{5647}\)
  1. 1405465835; locally 1910429:
    \(y = - \frac{1}{2} g t^2 + v_{0, y} t + y_0\)
    \(pdg_{5647} = - \frac{pdg_{1467}^{2} pdg_{1649}}{2} + pdg_{1467} pdg_{9107} + pdg_{1469}\)
LHS diff is pdg1467*(-pdg9107 + pdg9431) RHS diff is pdg1467*(-pdg9107 + pdg9431) 2461349007:
1405465835:
2461349007:
1405465835:
41 substitute LHS of expr 1 into expr 2
  1. 8949329361; locally 3041148:
    \(v_0 \sin(\theta) = v_{0, y}\)
    \(pdg_{5153} \sin{\left(pdg_{1575} \right)} = pdg_{9431}\)
  2. 1405465835; locally 1910429:
    \(y = - \frac{1}{2} g t^2 + v_{0, y} t + y_0\)
    \(pdg_{5647} = - \frac{pdg_{1467}^{2} pdg_{1649}}{2} + pdg_{1467} pdg_{9107} + pdg_{1469}\)
  1. 9862900242; locally 9780510:
    \(y = - \frac{1}{2} g t^2 + v_0 t \sin(\theta) + y_0\)
    \(pdg_{5647} = - \frac{pdg_{1467}^{2} pdg_{1649}}{2} + pdg_{1467} pdg_{5153} \sin{\left(pdg_{1575} \right)} + pdg_{1469}\)
LHS diff is 0 RHS diff is pdg1467*(-pdg5153*sin(pdg1575) + pdg9107) 8949329361:
1405465835:
9862900242: error for dim with 9862900242
8949329361:
1405465835:
9862900242: N/A
42 declare final expr
  1. 9862900242; locally 9780510:
    \(y = - \frac{1}{2} g t^2 + v_0 t \sin(\theta) + y_0\)
    \(pdg_{5647} = - \frac{pdg_{1467}^{2} pdg_{1649}}{2} + pdg_{1467} pdg_{5153} \sin{\left(pdg_{1575} \right)} + pdg_{1469}\)
no validation is available for declarations 9862900242: error for dim with 9862900242
9862900242: N/A
Physics Derivation Graph: Steps for equations of motion in 2D (calculus)

Symbols for this derivation

See also all 212 symbols
symbol ID category latex scope dimension name value Used in derivations references
5505 variable v_x
\(v_x\)
real
  • length: 1
  • time: -1
velocity along x axis
  • str_note
7
7055 variable a_y
\(a_y\)
real
  • length: 1
  • time: -2
acceleration along y axis 4
6373 variable \vec{v}
\(\vec{v}\)
real
  • length: 1
  • time: -1
velocity
  • str_note
2
1464 variable x
\(x\)
['real']
140
1572 variable x_0
\(x_0\)
['real']
  • length: 1
initial position 11
5647 variable y
\(y\)
['real']
  • length: 1
position 13
1700 variable \hat{y}
\(\hat{y}\)
real
unit vector 4
5674 variable d v_y
\(d v_y\)
['real']
  • length: 1
  • time: -1
differential velocity along y axis 2
5153 variable v_0
\(v_0\)
['real']
  • length: 1
  • time: -1
initial velocity 44
5842 variable dy
\(dy\)
['real']
  • length: 1
differential displacement along y axis
  • str_note
2
4711 variable dt
\(dt\)
['real']
  • time: 1
differential time
  • str_note
7
1467 variable t
\(t\)
['real']
  • time: 1
time 115
8339 variable \hat{x}
\(\hat{x}\)
real
unit vector 4
2423 variable \vec{a}
\(\vec{a}\)
real
  • length: 1
  • time: -2
acceleration
  • str_note
2
2958 variable v_{0, x}
\(v_{0, x}\)
['real']
  • length: 1
  • time: -1
initial velocity along x axis 15
1575 variable \theta
\(\theta\)
['real']
angle 34
1649 variable g
\(g\)
['real']
  • length: 1
  • time: -2
acceleration due to gravity 27
1469 variable y_0
\(y_0\)
['real']
  • length: 1
initial position 9
4037 variable x
\(x\)
['real']
  • length: 1
position 47
5005 variable d v_x
\(d v_x\)
['real']
  • length: 1
  • time: -1
differential velocity along x axis 2
9431 variable v_{0, y}
\(v_{0, y}\)
['real']
  • length: 1
  • time: -1
initial velocity along y axis 12
6091 variable \vec{v}_0
\(\vec{v}_0\)
['real']
  • length: 1
  • time: -1
initial velocity 1
7159 variable a_x
\(a_x\)
real
  • length: 1
  • time: -2
acceleration along x axis 4
9199 variable dx
\(dx\)
['real']
  • length: 1
15
9107 variable v_y
\(v_y\)
real
  • length: 1
  • time: -1
velocity along y axis
  • str_note
7
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