Linear Motion

1D kinematics: constant acceleration

POSITION
0.0 m
Δx = 0.0 m
VELOCITY
0.0 m/s
0 km/h
LIMIT
ACCELERATION
3.0 m/s²
1 segment
TIME
0.0 s
 
RUNNING
PARAMETERS
0.0 m
2.0 m/s
3.0 m/s²
Adjust the parameters and hit Start.
constant acceleration
(1)
(2)
auxiliary equations (when a ≠ 0)
(3)
(4)
GRAPHS scrubber line = current t
a × t
v × t
x × t
TIMELINE — drag to inspect any instant t = 0.0 s

📘 Conceptual notes

UNIFORM AND UNIFORMLY ACCELERATED MOTION IN ONE SIMULATION

In linear motion, the object travels along a straight line. When the acceleration is zero, you get uniform motion: velocity stays constant and position grows linearly with time (). When the acceleration is constant and non-zero, you get uniformly accelerated motion: velocity varies uniformly and position traces a parabola.

Notice how the a × t, v × t, and x × t graphs connect — the area under the v × t curve is exactly the displacement, and the slope of the x × t curve at any instant is the velocity.

🚗 Analogy: hitting the gas vs. braking
Stepping on the gas is a positive acceleration in the direction of motion: speed grows and the trail gets more and more spread out. Stepping on the brake is an acceleration opposite to the motion: the trail points cluster closer together until the car stops. If you keep braking past zero velocity, the car starts going in reverse — that's what happens when the acceleration has the opposite sign from the initial velocity.