The equation of a trajectory depends on the specific context and type of trajectory. Here are a few examples:

1. Projectile Motion:
- Horizontal trajectory: x(t) = v0x*t
- Vertical trajectory: y(t) = v0y*t - (1/2)_g_t^2
- Parabolic trajectory: y(x) = ax^2 + bx + c
2. Circular Motion:
- x(t) = r*cos(ωt + θ)
- y(t) = r*sin(ωt + θ)
3. Elliptical Motion:
- x(t) = a*cos(ωt + θ)
- y(t) = b*sin(ωt + θ)
4. Parametric Equations:
- x(t) = f(t)
- y(t) = g(t)

Where:

- x and y are the coordinates of the trajectory
- v0x and v0y are the initial velocities
- g is the acceleration due to gravity
- r is the radius
- ω is the angular frequency
- θ is the phase angle
- a and b are the semi-axes of the ellipse
- f and g are functions of time

In Advanced Level Maths, the equations of linear motion are:

1. Constant Acceleration:
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
s = displacement

1. Uniform Motion:
- s = vt
- v = s/t

Where:
s = distance
v = constant velocity
t = time

1. Motion with Variable Acceleration:
- dv/dt = a(t)
- v = ∫a(t)dt
- s = ∫v(t)dt

Where:
a(t) is the acceleration function
v(t) is the velocity function
s(t) is the position function

These equations describe linear motion in one dimension. In two or three dimensions, vector equations are used to describe motion.

In Advanced Level Maths, the equations of linear motion are:

1. Constant Acceleration:
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
s = displacement

1. Uniform Motion:
- s = vt
- v = s/t

Where:
s = distance
v = constant velocity
t = time

1. Motion with Variable Acceleration:
- dv/dt = a(t)
- v = ∫a(t)dt
- s = ∫v(t)dt

Where:
a(t) is the acceleration function
v(t) is the velocity function
s(t) is the position function

These equations describe linear motion in one dimension. In two or three dimensions, vector equations are used to describe motion.

In Advanced Level Maths, the equations of linear motion are:

1. Constant Acceleration:
- v = u + at
- s = ut + (1/2)at^2
- v^2 = u^2 + 2as

Where:
v = final velocity
u = initial velocity
a = acceleration
t = time
s = displacement

1. Uniform Motion:
- s = vt
- v = s/t

Where:
s = distance
v = constant velocity
t = time

1. Motion with Variable Acceleration:
- dv/dt = a(t)
- v = ∫a(t)dt
- s = ∫v(t)dt

Where:
a(t) is the acceleration function
v(t) is the velocity function
s(t) is the position function

These equations describe linear motion in one dimension. In two or three dimensions, vector equations are used to describe motion.