Kinematics

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velocityAfter Apas Cloud

The velocity after a time under constant acceleration, v = u + a t, as an exact quantity. Each argument's dimension is checked: a length where a velocity belongs is an error.

u (quantity) -- Initial velocity
a (quantity) -- Acceleration
t (quantity) -- Elapsed time

stateAfter Apas Cloud

Position and velocity after a time under constant acceleration along a line: x = x0 + u t + a t^2 / 2 and v = u + a t. Read them with s.position and s.velocity.

x0 (quantity) -- Initial position
u (quantity) -- Initial velocity
a (quantity) -- Acceleration
t (quantity) -- Elapsed time

timeToVelocity Apas Cloud

The time taken to go from one velocity to another under constant acceleration, t = (v - u) / a.

u (quantity) -- Initial velocity
v (quantity) -- Final velocity
a (quantity) -- Acceleration (not zero)

velocitySquaredAfter Apas Cloud

The square of the velocity after a displacement under constant acceleration, v^2 = u^2 + 2 a s. Take sqrt() of it for the speed; the direction is yours to choose.

u (quantity) -- Initial velocity
a (quantity) -- Acceleration
s (quantity) -- Displacement

trajectoryAt Apas Cloud

Position and velocity at a time for motion in a plane under constant acceleration (a projectile): r = r0 + v0 t + a t^2 / 2 and v = v0 + a t, exactly. Position, velocity and acceleration are [x, y] lists of quantities. Read the result with s.position and s.velocity; each is an [x, y] list.

r0 (list) -- Initial position [x, y]
v0 (list) -- Initial velocity [vx, vy]
a (list) -- Acceleration [ax, ay]
t (quantity) -- Elapsed time

trajectorySample Apas Cloud

The state of the same motion at each of a list of times: a list of records with time, position and velocity.

r0 (list) -- Initial position [x, y]
v0 (list) -- Initial velocity [vx, vy]
a (list) -- Acceleration [ax, ay]
times (list) -- The times, a list of quantities

timesAtX Apas Cloud

When the path reaches a given x, and the height y there: a list of records with time and y. There is one when x moves steadily, two when the motion in x turns back, and a sentence when the path never gets there. Times before the start (negative) are given too; keep the ones your problem allows.

r0 (list) -- Initial position [x, y]
v0 (list) -- Initial velocity [vx, vy]
a (list) -- Acceleration [ax, ay]
x (quantity) -- The x to reach