1D Motion & Kinematic Graphs
Drive a particle along a line and watch its x–t, v–t and a–t graphs draw in sync.
About this simulation
Set an initial velocity and acceleration and a particle moves along a track while three stacked graphs — position, velocity and acceleration versus time — build together under a shared time cursor. The area under the v–t graph is shaded as it builds, so "which a–t graph matches this v–t?" becomes something to watch rather than deduce.
How to use it
- Set the Initial velocity and Acceleration sliders and watch the particle move along the track while the x–t, v–t and a–t graphs draw in step under one time cursor.
- Tap Uniform velocity under Try: the x–t graph is a straight sloping line, the v–t graph is flat and the a–t graph sits on zero.
- Tap Uniform acceleration and see the x–t graph curve upward while the v–t graph becomes a straight sloping line.
- Tap Free fall and watch v pass through zero while a stays at −9.8 m/s²; the shaded area under the v–t graph turns negative later in the run.
- Switch Profile to Accel, then brake to see the a–t graph jump from +a to −a halfway through the 6-second run.
What to notice
- The slope of the x–t graph at any instant is the velocity at that instant.
- The slope of the v–t graph is the acceleration, and the shaded area under it is the displacement so far.
- Velocity can be zero while acceleration is not, as at the turning point in the Free fall preset.
- Displacement in 6 s can be negative or smaller than the distance travelled when the particle reverses direction.
The formulas
- v = u + at
- Velocity v at time t for initial velocity u and constant acceleration a.
- s = ut + ½at²
- Displacement s after time t under constant acceleration a.
- v̄ = s / t
- Average velocity v̄ is total displacement s divided by the time taken t.
Questions
What does the slope of a position-time graph tell you?
The slope of an x–t graph at any point is the instantaneous velocity. A straight line means constant velocity, a steeper line means faster motion, a downward slope means motion in the negative direction, and a curving graph means the velocity is changing. In the simulation, watch the x–t curve flatten exactly when the velocity readout passes through zero.
What does the area under a velocity-time graph represent?
The area between a v–t graph and the time axis is the displacement. Area above the axis counts as positive and area below it as negative, so if the object turns back, the net area can be smaller than the distance travelled. In the simulation, the shaded region under the v–t graph grows as time runs, and at 6 s it matches the x value shown at the top right.
Can a body have zero velocity and non-zero acceleration?
Yes. A ball thrown straight up has zero velocity at its highest point, yet its acceleration is still g downwards, which is why it immediately starts to fall. On graphs, the v–t line crosses zero while the a–t line stays at a constant non-zero value. In the simulation, the Free fall preset (u = 15 m/s, a = −9.8 m/s²) shows exactly this at about 1.5 s.
What do the motion graphs look like for uniformly accelerated motion?
For constant acceleration, the a–t graph is a horizontal line, the v–t graph is a straight line whose slope equals a, and the x–t graph is a parabola that curves upward for positive a and downward for negative a. In the simulation, tap Uniform acceleration (u = 0, a = 4 m/s²) and compare the three graphs as they draw.
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