Moving cart
What you will learn: how the shape of the position-time, velocity-time and acceleration-time graphs tells you how an object moves.
Track (−10 m to +10 m)
t0.0 s
x0.0 m
v0.0 m/s
a0.0 m/s²
Mode:
Keyboard: space = play/pause, r = reset.
Presets:
Press on the track and drag the cart left and right. The clock starts when you first touch it and runs for 10 s. Let go and the cart stays still. v and a are estimated from your drag (slope of x, then slope of v), lightly smoothed, so they look a bit noisy.
Motion graphs (0 to 10 s)
Slope of the x-t graph = velocity. Slope of the v-t graph = acceleration. Area under the v-t graph = displacement (change in position).
Try this
- Click Constant speed right, then Play. What shape is the position-time graph, and what does the velocity-time graph look like?
The x-t graph is a straight slanted line: the same change in position every second. Its slope (1.5 m/s) is the velocity, so the v-t graph is a flat horizontal line at 1.5 m/s and the a-t graph sits at 0. - Click Speeding up. Why does the position-time graph curve upward instead of being a straight line?
The cart covers more distance each second, so the slope of the x-t graph keeps getting steeper. A steeper slope means a larger velocity. The v-t graph is a straight line going up, and its slope is the constant acceleration (0.4 m/s²). - Click Slowing down then turning around. At the moment the cart turns around, what are its velocity and acceleration? Where do you see this on each graph?
At t = 5 s the velocity is 0 (the v-t line crosses the time axis, and the x-t graph has its flat top). The acceleration is still −0.6 m/s², not zero: the a-t graph stays flat below zero the whole time. Zero velocity does not mean zero acceleration.