One object, three graphs, one clock.
Set an initial position, velocity and constant acceleration. The cart, the x-t, v-t and a-t graphs all read from the same time value, so you can see slope and area become motion.
Constant acceleration
- Position x
- 0 m
- Velocity v
- 12 m/s
- Displacement
- 0 m
- Distance
- 0 m
- Live run (B)
Drag on any graph to scrub time. The slope of x(t) is v; the slope of v(t) is a; the area under v(t) is displacement.
Constant acceleration
x(t) = x0 + v0 t + (1/2) a t^2, v(t) = v0 + a t, a(t) = a.
The slope of the position graph at any instant is the velocity. The slope of the velocity graph is the acceleration. The signed area under v(t) is the displacement.
When v0 and a have opposite signs the object slows, stops at t = -v0 / a and turns around. Displacement then differs from distance travelled.
Turnaround preset
x0 = 10 m, v0 = 12 m/s, a = -3 m/s^2. Turning time: t = 12 / 3 = 4 s.
x(4) = 10 + 48 - 24 = 34 m. x(10) = 10 + 120 - 150 = -20 m.
Displacement over 10 s: -30 m. Distance: 24 m forward + 54 m back = 78 m. Load the preset and scrub to 4 s to check.