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Motion Diagrams

Explore graphs of linear and circular motion.

ULM · Uniform linear motion

Velocity stays constant over time, so the graph is horizontal. The area beneath it gives displacement.

Motion graph

v (m/s) vs t (s)v\,(\mathrm{m/s})\text{ vs }t\,(\mathrm{s})

v (m/s)v\,(\mathrm{m/s})
t (s)t\,(\mathrm{s})
Velocity graphed over time. At 6 seconds, the velocity is 5 meters per second.
6 s6\,\mathrm{s}
010
5 m/s5\,\mathrm{m/s}
412

Velocity at t=6 st = 6\,\mathrm{s}

5 m/s5\,\mathrm{m/s}

Area under graph (Δx\Delta x)

30 m30\,\mathrm{m}

Graph: v(t)=v0v(t) = v_0

Area: Δx=v0t\Delta x = v_0 t

UALM · Uniformly accelerated linear motion

Constant acceleration makes velocity change linearly. The line's slope is acceleration, and the area beneath it is displacement.

Motion graph

v (m/s) vs t (s)v\,(\mathrm{m/s})\text{ vs }t\,(\mathrm{s})

v (m/s)v\,(\mathrm{m/s})
t (s)t\,(\mathrm{s})
Velocity graphed over time. At 6 seconds, the velocity is 8.6 meters per second.
6 s6\,\mathrm{s}
010
5 m/s5\,\mathrm{m/s}
412
0.6 m/s20.6\,\mathrm{m/s^2}
-0.41.2

Velocity at t=6 st = 6\,\mathrm{s}

8.6 m/s8.6\,\mathrm{m/s}

Area under graph (Δx\Delta x)

40.8 m40.8\,\mathrm{m}

Graph: v(t)=v0+atv(t) = v_0 + at

Area: Δx=v0t+12at2\Delta x = v_0 t + \frac{1}{2}at^2

UCM · Uniform circular motion

Angular velocity stays constant over time. Its graph is horizontal, and the area beneath it gives angular displacement.

Motion graph

ω (rad/s) vs t (s)\omega\,(\mathrm{rad/s})\text{ vs }t\,(\mathrm{s})

ω (rad/s)\omega\,(\mathrm{rad/s})
t (s)t\,(\mathrm{s})
Angular velocity graphed over time. At 6 seconds, the angular velocity is 2.5 radians per second.
6 s6\,\mathrm{s}
010
2.5 rad/s2.5\,\mathrm{rad/s}
26

Angular velocity at t=6 st = 6\,\mathrm{s}

2.5 rad/s2.5\,\mathrm{rad/s}

Area under graph (Δθ\Delta\theta)

15 rad15\,\mathrm{rad}

Graph: ω(t)=ω0\omega(t) = \omega_0

Area: Δθ=ω0t\Delta\theta = \omega_0 t

UACM · Uniformly accelerated circular motion

Constant angular acceleration makes angular velocity change linearly. The line's slope is angular acceleration, and the area beneath it is angular displacement.

Motion graph

ω (rad/s) vs t (s)\omega\,(\mathrm{rad/s})\text{ vs }t\,(\mathrm{s})

ω (rad/s)\omega\,(\mathrm{rad/s})
t (s)t\,(\mathrm{s})
Angular velocity graphed over time. At 6 seconds, the angular velocity is 4.3 radians per second.
6 s6\,\mathrm{s}
010
2.5 rad/s2.5\,\mathrm{rad/s}
26
0.3 rad/s20.3\,\mathrm{rad/s^2}
-0.20.6

Angular velocity at t=6 st = 6\,\mathrm{s}

4.3 rad/s4.3\,\mathrm{rad/s}

Area under graph (Δθ\Delta\theta)

20.4 rad20.4\,\mathrm{rad}

Graph: ω(t)=ω0+αt\omega(t) = \omega_0 + \alpha t

Area: Δθ=ω0t+12αt2\Delta\theta = \omega_0 t + \frac{1}{2}\alpha t^2