Recognizing URM on a Graph

The distance-time graph

For uniform rectilinear motion, if you plot the distance traveled d as a function of time t, you always get a straight line passing through the origin (if the object starts from zero). The steeper the slope of this line, the greater the speed, because the slope of the d(t) graph precisely represents the speed v.

The speed-time graph

If you plot the speed v as a function of time t for a URM, you get a horizontal line: the speed does not change, it remains constant regardless of the value of t.

Type of graph	Shape for a URM
Distance as a function of time	Oblique line passing through the origin
Speed as a function of time	Horizontal line

Concrete example

A robot moves forward at constant speed. After 2 s it has traveled 4 m, after 4 s it has traveled 8 m, after 6 s it has traveled 12 m. The distances double when the time doubles: this is indeed a URM, with speed v = 4 / 2 = 2 m/s.

Common pitfalls to avoid

A distance-time graph that is a curve (and not a straight line) means the motion is not uniform: the speed changes over time. Also, do not confuse a horizontal line on a distance-time graph (the object is stationary, its distance no longer changes) with a horizontal line on a speed-time graph (the object is moving at constant speed).