☰ Contents · Physics

Graphs of uniform motion. Non-uniform motion

Lessons 7–8 · 2 lessons · P.Q. Habibullayev, A. Boydedayev, A.D. Bahromov, S.O. Burxonov. Physics Grade 7, revised and enlarged 4th edition. “O‘zbekiston milliy ensiklopediyasi” State Scientific Publishing House, Tashkent, 2017
7

Graphs of uniform rectilinear motion

Textbook: pp. 32–33
GoalUnderstand and read the distance–time and velocity–time graphs of uniform motion.
New words
graph · grafikdistance–time graph · yo‘l grafigivelocity–time graph · tezlik grafigicoordinate axes · koordinata o‘qlari
Explanation

On a graph the horizontal axis shows time t and the vertical axis shows distance s (or velocity υ). In uniform motion s = υt, so the distance–time graph is a slanted straight line starting at the origin: the steeper the line, the greater the velocity. The velocity–time graph is a horizontal straight line parallel to the time axis, because the velocity does not change. The area of the rectangle under the velocity graph equals υ · t, i.e. the distance covered. To find the distance at a given time from the graph, go up from that time to the line and then across to the distance axis. If a coordinate–time (x–t) graph starts not at the origin but at some point on the x axis, the body was away from the origin at the start.

Worked examples
If a body covers 6 m in 2 s, 12 m in 4 s and 18 m in 6 s, the distance graph is a straight line through the origin; υ = 6 : 2 = 3 m/s.
If the velocity graph is a horizontal line at 4 m/s, the distance in 5 s equals the rectangle area: 4 · 5 = 20 m.
Class activity

“Describe the graph in words”: the teacher draws two slanted lines (one steeper); pupils say which body is faster and why. Safety: use only chalk or markers.

Practice
1
What does the distance–time graph of uniform motion look like?
2
What does the velocity–time graph look like?
3
The velocity is 3 m/s for 8 s. What are the area under the graph and the path in metres?
4
Why is the distance graph of a faster body steeper?