What the Shape of a Line Tells You About a Journey
Learn to tell uniform motion from non-uniform, calculate speed in m/s and km/h, find average speed, and read a distance-time graph at a glance.
What is the difference between uniform and non-uniform motion?
An object is in uniform linear motion when it covers equal distances in equal intervals of time, moving in a straight line. If the distances covered in equal intervals differ, the motion is non-uniform.
This page covers everything in the CBSE Class 7 Science chapter's second half: telling the two kinds of motion apart, calculating speed and converting its units, finding average speed, and reading a distance-time graph.
This page covers everything in the CBSE Class 7 Science chapter's second half: telling the two kinds of motion apart, calculating speed and converting its units, finding average speed, and reading a distance-time graph.
How do you tell from readings whether motion is uniform?
Compare the distance covered in each equal time interval.
A car covering 20 m every second — 20 m, 40 m, 60 m, 80 m after each successive second — is in uniform motion, because each interval adds the same 20 m.
A car covering 20 m, then 35 m, then 15 m, then 45 m in successive seconds is in non-uniform motion, since the distances differ.
In real life, almost all everyday motion is non-uniform: a bus on an Indian road speeds up, slows for traffic and stops at signals, so it rarely covers equal distances in equal times for long.
Uniform motion does not mean the object is fast, and non-uniform does not mean it is slow. A vehicle crawling steadily at 5 km/h is in uniform motion, while one alternating between 60 and 80 km/h is not.
A car covering 20 m every second — 20 m, 40 m, 60 m, 80 m after each successive second — is in uniform motion, because each interval adds the same 20 m.
A car covering 20 m, then 35 m, then 15 m, then 45 m in successive seconds is in non-uniform motion, since the distances differ.
In real life, almost all everyday motion is non-uniform: a bus on an Indian road speeds up, slows for traffic and stops at signals, so it rarely covers equal distances in equal times for long.
Uniform motion does not mean the object is fast, and non-uniform does not mean it is slow. A vehicle crawling steadily at 5 km/h is in uniform motion, while one alternating between 60 and 80 km/h is not.
Formula
How do you calculate speed and convert its units?
Speed is the distance travelled in one unit of time:
Its SI unit is metre per second (m/s), and it is also commonly measured in kilometre per hour (km/h).
Worked example. A cyclist covers 150 m in 30 s:
To convert, note that 1 km is 1000 m and 1 hour is 3600 s, so 1 km/h is m/s:
So 72 km/h is m/s, and our cyclist's 5 m/s is km/h.
Units must match before dividing. Distance in metres with time in hours gives a number in no standard unit at all.
Its SI unit is metre per second (m/s), and it is also commonly measured in kilometre per hour (km/h).
Worked example. A cyclist covers 150 m in 30 s:
To convert, note that 1 km is 1000 m and 1 hour is 3600 s, so 1 km/h is m/s:
So 72 km/h is m/s, and our cyclist's 5 m/s is km/h.
Units must match before dividing. Distance in metres with time in hours gives a number in no standard unit at all.
Formula
How do you find distance, time and average speed?
Rearranging the speed relation gives the other two quantities:
A train travelling at 60 km/h for 3 hours covers km. To cover 240 km at 80 km/h takes hours.
Average speed is the total distance divided by the total time for the whole journey:
A bus covers 100 km in 2 hours and then 150 km in 3 hours. Total distance 250 km, total time 5 hours, so the average speed is km/h.
A vehicle's speedometer shows its speed at that instant, while its odometer shows the total distance it has travelled. Reading the odometer at the start and end of a trip gives the distance you need for an average-speed calculation.
A train travelling at 60 km/h for 3 hours covers km. To cover 240 km at 80 km/h takes hours.
Average speed is the total distance divided by the total time for the whole journey:
A bus covers 100 km in 2 hours and then 150 km in 3 hours. Total distance 250 km, total time 5 hours, so the average speed is km/h.
A vehicle's speedometer shows its speed at that instant, while its odometer shows the total distance it has travelled. Reading the odometer at the start and end of a trip gives the distance you need for an average-speed calculation.
How do you read a distance-time graph?
Plot time along the horizontal axis and distance along the vertical axis, mark each reading as a point, and join them.
The shape of the line tells you the motion immediately:
- a straight sloping line means uniform motion — equal distances in equal times
- a steeper straight line means a greater speed, since more distance is covered in the same time
- a horizontal line means the object is at rest — time passes but distance does not increase
- a curved line means non-uniform motion, with speed changing
For example, a graph of a train journey might rise steadily, flatten while the train stands at a station, then rise steeply again as it speeds up after leaving.
Read values off the graph by going up from a time to the line and across to the distance axis.
The horizontal line is the one students misread. A flat line does not mean the object has vanished or returned — it means it stayed at the same distance while time continued, which is exactly what standing still looks like.
The shape of the line tells you the motion immediately:
- a straight sloping line means uniform motion — equal distances in equal times
- a steeper straight line means a greater speed, since more distance is covered in the same time
- a horizontal line means the object is at rest — time passes but distance does not increase
- a curved line means non-uniform motion, with speed changing
For example, a graph of a train journey might rise steadily, flatten while the train stands at a station, then rise steeply again as it speeds up after leaving.
Read values off the graph by going up from a time to the line and across to the distance axis.
The horizontal line is the one students misread. A flat line does not mean the object has vanished or returned — it means it stayed at the same distance while time continued, which is exactly what standing still looks like.
Exam tip
Exam tip: choosing the scale before you plot
Most marks lost on graph questions go on the scale, not the points.
Decide the scale from the largest value on each axis and the space available. If distances run up to 300 m across about 6 cm, take 1 cm = 50 m. Use round numbers — 1, 2, 5, 10, 20, 50 — never something like 1 cm = 35 m.
Then label both axes with their quantity and unit, write the scale on the graph, and give the graph a title. An unlabelled graph cannot be marked even when every point is plotted perfectly.
Finally, start the distance axis at zero unless told otherwise, or the slopes will misrepresent the speeds.
Decide the scale from the largest value on each axis and the space available. If distances run up to 300 m across about 6 cm, take 1 cm = 50 m. Use round numbers — 1, 2, 5, 10, 20, 50 — never something like 1 cm = 35 m.
Then label both axes with their quantity and unit, write the scale on the graph, and give the graph a title. An unlabelled graph cannot be marked even when every point is plotted perfectly.
Finally, start the distance axis at zero unless told otherwise, or the slopes will misrepresent the speeds.
Did you know
Why does a steeper line on a distance-time graph mean faster motion?
The slope of the line is simply distance divided by time — which is the definition of speed.
A steep line climbs a lot of distance in a small stretch of time, giving a large value, while a gentle line covers little distance over the same time. So the graph does not merely represent speed; its slope is the speed.
A steep line climbs a lot of distance in a small stretch of time, giving a large value, while a gentle line covers little distance over the same time. So the graph does not merely represent speed; its slope is the speed.
Key takeaways
Motion and speed: quick revision
- Uniform motion covers equal distances in equal time intervals; unequal distances mean non-uniform motion, and neither term is about being fast or slow.
- speed = distance ÷ time, measured in m/s or km/h; multiply by 5/18 to convert km/h to m/s and by 18/5 to go back.
- distance = speed × time and time = distance ÷ speed; average speed is total distance ÷ total time, never the average of two speeds.
- A speedometer shows speed at that instant; an odometer shows total distance travelled.
- On a distance-time graph a straight slope means uniform motion, a steeper slope means greater speed, a horizontal line means at rest, and a curve means changing speed.
You will remember all of this far better after answering five questions on it than after reading it twice.
- speed = distance ÷ time, measured in m/s or km/h; multiply by 5/18 to convert km/h to m/s and by 18/5 to go back.
- distance = speed × time and time = distance ÷ speed; average speed is total distance ÷ total time, never the average of two speeds.
- A speedometer shows speed at that instant; an odometer shows total distance travelled.
- On a distance-time graph a straight slope means uniform motion, a steeper slope means greater speed, a horizontal line means at rest, and a curve means changing speed.
You will remember all of this far better after answering five questions on it than after reading it twice.