The orange arrows are the path travelled. The purple arrow is the displacement: from where the cart started to where it is now.
Right is positive. Distance adds up every move and is never negative; displacement = final position − initial position.
Time t
0.00 s
Position x
0.00 m
Velocity v
2.00 m/s
Acceleration a
0.00 m/s²
Drag the cart to set its starting position, and drag the green arrow to set its starting velocity. Drag across any graph to replay the motion at that moment.
The track's scale grows to fit the motion. Faint carts show where it was at each whole second. The simulation runs from 0 to 10 s.
Worked example (notes p. 2-40)
A car travelling to the right at 20 m/s brakes uniformly to 8.0 m/s in 4.0 s. (Right is positive.) Find the acceleration. Find the deceleration.
Accelerationa = (v − u) ÷ t = (8.0 − 20) ÷ 4.0 = −3.0 m/s². Acceleration is a vector: keep the sign.
Deceleration = 3.0 m/s². The word already means slowing down, so give the size only.
Press Pause, then Next key moment to stop at t = 4.0 s and read v = 8.00 m/s.
Position–Time Graph, x–t
Velocity–Time Graph, v–t
Acceleration–Time Graph, a–t
Key features (tap one)
Positive or negative? (notes p. 2-40)
Right and up are positive.
Velocity, displacement and acceleration keep their sign: negative means opposite to your positive direction.
Speed, distance and deceleration are sizes only: the word already gives the direction.
A car slowing down while moving right has a negative acceleration.
“The minus sign and the word ‘deceleration’ do the same job. Use one, never both.”