Lesson 3-2. Travel graphs

This section covers travel graphs, speed, distance, time and velocity.

Speed, Distance and Time.

The following is basic but important formula which applies when speed is constant (in other words the speed doesn’t change).

Remember, when using any formula, the units must all be consistent.

For example speed could be measured in m/s, distance in metres and time in seconds.

If speed does change, the average (mean) speed can be calculated:

Units.

In calculations, units must be consistent, so if the units in the question are not all the same (e. g. m/s, m and s or km/h, km and h), change the units before starting, as above.

The following is an example of to change the units:

EXAMPLE:

Change 15 km/h into m/s.

15 km/h = 15/60 km/min =

15/3600 km/s = 1/240 km/s

 = 1000/240 m/s = 4.167 m/s

Travel graphs are line graphs that are used to describe the motion of objects such as cars, trains, walkers and cyclists. The distance travelled is represented on the vertical axis and the time taken to travel that distance is represented on the horizontal axis.

EXAMPLE:

The following graph gives the distance of a cyclist from his home.

a. When did the cyclist leave home?

b. When did the cyclist return home?

c. How far away from home was he at 10 a.m.?

d. How far away from home was he at 11 a.m.?

e. How far away from home was he at 2 p.m.?

f. How far away from home was he at 3 p.m.?

g. At what times did he take arrest?

h. How far away from home was he at noon?

i. How far away from home was he at 5 p.m.?

j. Find his speed from:

(i)  8 a.m. to 10 a.m.

(ii)  11 a.m. to 2 a.m.

(iii)  3 a.m. to 5 a.m.

k. When was the cyclist travelling most quickly?

SOLUTION:

a. The cyclist left home at 8 a.m.

b. The cyclist returned home at 5 a.m.

c. At 10 a.m., he was 20 km away from home.

d. At 11 a.m., he was 20 km away from home.

e. At 2 p.m., he was 60 km away from home.

f. At 3 p.m., he was 60 km away from home.

g. The cyclist took a rest between 10 a.m. and 11 a.m. and between 2 p.m. and 3 p.m.

h. At noon, he was about 33 km away from home.

i. At 5 p.m., the cyclist was at home. So, he was 0 km away from home.

j. Find his speed from:

j. (i) Speed from 8 a.m. to 10 a.m. =

j. (ii) Speed from 11 a.m. to 1 p.m. =

j. (iii) Speed from 3 p.m. to 5 p.m. =

k. The cyclist was travelling most quickly between 3 p.m. and 5 p.m.

Lesson 3-2

•  Test 1 
•  Test 2
•  Test 3