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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

Curve

x(t)—

y(t)—

rₓ

—

rᵧ

—

|r⃗|

—

v⃗ hodograph

Curve

ẋ(t)—

ẏ(t)—

vₓ

—

vᵧ

—

|v⃗|

—

a⃗ acc-space

Curve

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×