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Vector Kinematics — r⃗ · Δr⃗ · v⃗ · a⃗

Position · Displacement · Velocity · Acceleration

XY PLANE
Concept Mode
r⃗(t)
Δr⃗
v⃗
a⃗
Concept
The position vector r⃗(t) points from origin O to the ball at every instant. r⃗(t) = x(t) î + y(t) ĵ
Live Values
x(t)
—
y(t)
—
|r⃗|
—
|Δr⃗|
—
|v⃗|
—
|a⃗|
—
Controls
Δt (displacement gap)0.80 s
Speed1.0×
Legend
Full path trail (always shown)
r⃗(t) — position vector
Δr⃗ — displacement
v⃗ — velocity
a⃗ — acceleration
💡 Trail shows the complete path at all times. Shrink Δt → watch Δr⃗ align with v⃗!
r⃗   position
x(t)—
y(t)—
rₓ
—
rᵧ
—
|r⃗|
—
v⃗   hodograph
ẋ(t)—
ẏ(t)—
vₓ
—
vᵧ
—
|v⃗|
—
a⃗   acc-space
ẍ(t)—
ÿ(t)—
aₓ
—
aᵧ
—
|a⃗|
—
|r⃗|(t) POSITION MAGNITUDE
now
—
min
—
max
—
|v⃗|(t) VELOCITY MAGNITUDE
now
—
min
—
max
—
|a⃗|(t) ACCELERATION MAGNITUDE
now
—
min
—
max
—
Δt0.80s
Speed1.0×