Feroz and his sister Sania go to school on their bicycles. Both of them start at the same time from their home but take different times to reach the school although they follow the same route. Table 8.5 shows the distance travelled by them in different times
Answers
Feroz and his sister Sania go to school on their bicycles. Both of them start at the same time from their home but take different times to reach the school although they follow the same route. Table 8.5 shows the distance travelled by them in different times
Explanation:
The Distance-time graph of the travel made by Feroz is indicated in yellow.
• The Distance-time graph of the travel made by Sania is indicated in cyan.
• In the x-axis, only minutes are taken. If we take hours too, we will have to convert into decimal form as follows:
8:05 = 8 + 5/60 = 8 + 0.08333 = 8.08333
8:10 = 8 + 10/60 = 8 + 0.16667 = 8.16667
8:15 = 8 + 15/60 = 8 + 025 = 8.25
• Therefore it more suitable to take minutes alone
• Once the scales on x and y axes are fixed, we can plot the graphs easily. The coordinates can be taken directly from the table. No calculation will be required.
Interpretation:
• Feroz was travelling at a greater speed since he travelled 3.6 Kms in 20 minutes, while Sania took 25 minutes to cover the same distance.
• After the plotting, if we examine carefully, we discover that, the points do not fall on straight lines.
• This will be seen if we join the first and last points separately for the two graphs. It is shown in the fig.1.30 below:
Distance time graph showing that speed is not uniform
Fig.1.30
• The dashed lines are used to join the first and last points. This is to enables us distinguish from the main graph.
• Since they are not straight lines, we can infer:
♦ Feroz did not travel at an uniform speed
♦ Sania did not travel at an uniform speed
Reason:
■ If the travel is at an uniform speed, we must get similar triangles for any random pairs of points that we take in a Distance-time graph. So that the ratio altitude⁄base is always a constant. If it is not a straight line, we will not get similar triangles at any random pair we take. As we saw in fig.1.15
■ From the readings in the given table, it is evident that the speeds were not uniform:
Feroz travelled 1 Km in the first 5 minutes
He travelled (1.9 - 1) = 0.9 Km in the next 5 minutes
He travelled (2.8 - 1.9) = 0.9 Km in the next 5 minutes
He travelled (3.6 - 2.8) = 0.8 Km in the next 5 minutes
■ Sania travelled 0.8 Km in the first 5 minutes
She travelled (1.6 - 0.8) = 0.8 Km in the next 5 minutes
She travelled (2.3 - 1.6) = 0.7 Km in the next 5 minutes
She travelled (3.0 - 2.3) = 0.7 Km in the next 5 minutes
She travelled (3.6 - 3.0) = 0.6 Km in the next 5 minutes
