Drag points to shape a distance-time or velocity-time graph and a runner moves to match. See why slope is speed or acceleration, and the area under a velocity-time line is distance.
At t = 0 s
speed = 2 m/s
slope of the line (moving forward)
Distance: 1 m
On a distance-time graph the SLOPE is the speed: steeper means faster, flat means stopped, and a downward slope means moving back toward the start.
Drag the dots (or focus one and use the arrow keys) to reshape the motion.
Reading motion from a graph
A graph can tell the whole story of a moving object: where it is, how fast it goes,
and whether it speeds up or slows down. The interactive above lets you drag the
points to shape a distance-time or velocity-time graph, and a runner moves
along a track to match. Press Play to watch the motion trace out in real time. The
key to reading any motion graph is the same idea you meet in math: the slope of the
line.
Speed and velocity: what is actually moving
Speed is how fast something moves (for example 5 m/s). Velocity is speed plus a
direction. On a graph, a positive slope and a negative slope are both real motion, just
in opposite directions, which is why velocity, not just speed, is what physics tracks.
Distance-time graphs: slope is speed
On a distance-time graph, time runs along the bottom and distance up the side. The
slope of the line is the speed:
A steep line means fast.
A gentle line means slow.
A flat (horizontal) line means stopped.
A line sloping down means moving back toward the start.
Velocity-time graphs: slope is acceleration, area is distance
Switch the graph to Velocity-time. Now the height of the line is the velocity itself,
and two new ideas appear:
The slope of the line is the acceleration (how quickly the velocity changes).
Sloping up is speeding up; sloping down is slowing down; flat is constant velocity.
The area under the line is the distance travelled. A constant velocity traces a
rectangle (velocity times time); a changing velocity traces a triangle or trapezoid.
Why this connects to math
“Slope = speed” and “slope = acceleration” are the same slope you compute
on a coordinate plane: rise over run. Motion graphs are just a
coordinate plane where the x-axis is time. Once you can read a slope, you can read motion.
Using this with a class
Call out a motion in words (“she walks fast, stops to tie a shoe, then jogs home”) and
have students build the distance-time graph to match, then check with Play. Or give a
velocity-time graph and ask for the distance (the area) before revealing the readout.
It is free to embed on your own site or LMS.
Frequently asked questions
What does the slope of a distance-time graph represent?
The slope of a distance-time graph is the speed. A steep slope means fast motion, a gentle slope means slow motion, a flat (horizontal) line means the object is stopped, and a downward slope means it is moving back toward the start. Slope is rise over run, which here is distance divided by time, and distance over time is exactly speed.
What does the slope of a velocity-time graph represent?
The slope of a velocity-time graph is the acceleration. A line sloping up means speeding up (positive acceleration), a line sloping down means slowing down, and a flat line means constant velocity (zero acceleration). Slope here is change in velocity divided by time, which is the definition of acceleration.
What does the area under a velocity-time graph represent?
The area between a velocity-time line and the time axis is the distance travelled (displacement). For a constant velocity the area is a rectangle (velocity times time); for changing velocity it is a triangle or trapezoid. This works because distance equals velocity times time, and that product is exactly the area under the line.
What is the difference between speed and velocity?
Speed is how fast something moves (a scalar, just a number with a unit like m/s). Velocity is speed together with a direction (a vector). A car going around a roundabout at a steady 30 km/h has constant speed but changing velocity, because its direction keeps changing. A change in velocity is an acceleration, so turning is a kind of acceleration even at constant speed.
How do you find acceleration from a velocity-time graph?
Find the slope of the line: pick two points, take the change in velocity (rise) and divide by the change in time (run). For example, if velocity goes from 2 m/s to 8 m/s over 3 seconds, the acceleration is (8 - 2) / 3 = 2 m/s squared. A steeper line means a larger acceleration.