Date: …………………….. UNIT: Travel Graphs Worksheet
Name: Grade 10/… OBJECTIVES:
1. Draw and interpret Distance-Time graphs.
2. Calculate Speed.
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PART I: Distance-Time Graphs
• Speed is represented by the gradient of a distance-time graph.
Ave speed = ���������� ���������������� ������������������
��
��
���������� �������� ���������� ie S =
• The steeper the graph, the greater the speed.
• A horizontal line on a “DISTANCE-TIME Graph” indicates no gradient and hence no
speed (ie. AT REST)
Examples:
1. A train travelled 500km at an average speed of 80km/h. How long did the journey last?
S = ���� therefore, Time = Distance
Speed
= 500 ÷ 80
= 6.25
hours or 6 hours & 15 minutes
………………………………………………………………………………………..……………
2. A cyclist travelled for 90 minutes at an average speed of 20km/hr. He then travelled for an
additional 30 minutes at an average speed of 30km/hr. What was his average speed for the entire
journey? (Hint: not 25km/hr)
S = ���� therefore, D = S × T
• distance of first stage of the journey = 20 × 1.5hrs = 30km (90minutes ÷ 60 = 1.5hrs) •
distance of the second stage = 30 × 0.5hrs = 15km (30minutes ÷ 60 = 0.5hrs)
Hence, Total Distance = 30 + 15 = 45km & Total Time = 1.5 + 0.5 = 2hours
Ave speed = ���������� ���������������� ������������������
���������� �������� ���������� = 45km ÷ 2hrs
= 22.5
km/hr
…………………………………………………………………………………………………
3. The distance-time graph below shows the three stage journey of a car travelling from Town A to
Town C and back to Town A.
(a) State the time of day at which the car arrived at Town C …0830
or 8:30 am…
(b) State the total distance between Towm A and Town C … 100km……
(c) Calculate the TOTAL time, in minutes, for which the car stopped during the journey.
Scale of time axis: 1cm = 15minutes
Therefore, Total Time stopped = 30minutes+ 15minutes = 45
minutes
.....................................................................................................................................
(d) Determine the constant speed of the car during:
i) Stage 2 of the journey ii) Stage 3 of the journey
S = ����
Speed = (100 – 40) Speed = (100 - 0)_
(8:30–7:30) (10:00-8:45) {75mins÷60=1.25hrs}
= 60km/hr
=100÷1.25= 80km/hr ……………………………………
…………………………………….
(e) Calculate the average speed of the car for the time during which it was moving Total
distance = 100 + 100 = 200km & Total time moving = 1 + 1 + 1.25 = 3.25hrs
Ave speed = ���������� ���������������� ������������������
���������� �������� ���������� =
200km ÷ 3.25hrs = 61.5km/hr
………………………………………………………………………………………..
4. A Plane travels 400km in the first 50 minutes of a journey, the next 300km in 30 minutes and the
final 500km in 40 minutes.
i) Find the total Distance of the Plane’s journey: (1mark) 400km + 300km + 500km = 1
200km
……………………………………………………………………………………………….
ii) Determine the total time taken for the entire journey: (1 mark)
50mins + 30mins + 40mins = 120mins = 2hours
………………………………………………………………………………………………..
iii) Draw a distance-time graph on graph paper to represent the journey, using a scale of 1cm=
100km on the y-axis and 1cm= 10minutes on the x-axis.
(6
marks)
iv) Hence determine the average speed of the entire journey
Ave speed = ���������� ���������������� ������������������
���������� �������� ���������� = 1 200km ÷ 2hrs = 600km/hr
……………………………………………………………………………………(2marks)