Cambridge Additional Mathematics

Applications of integration (Chapter 16) 445

Example 7 Self Tutor

The velocity-time graph for a train journey is

illustrated in the graph alongside. Find the total

distance travelled by the train.

Total distance travelled

=total area under the graph

=area A+area B+area C+area D+area E

=^12 (0:1)50 + (0:2)50 +

¡50+30

2

¢

(0:1) + (0:1)30 +^12 (0:1)30

=2:5+10+4+3+1: 5

=21km

EXERCISE 16C.1

1 A runner has the velocity-time graph shown. Find the

total distance travelled by the runner.

2 A car travels along a straight road with the velocity-time

function illustrated.

a What is the significance of the graph:

i above thet-axis

ii below thet-axis?

b Find the totaldistancetravelled by the car.

c Find the final displacementof the car from its

starting point.

3 A cyclist rides off from rest, accelerating at a constant rate for

3 minutes until she reaches 40 km h¡^1. She then maintains a

constant speed for 4 minutes until reaching a hill. She slows

down at a constant rate over one minute to 30 km h¡^1 , then

continues at this rate for 10 minutes. At the top of the hill

she reduces her speed uniformly and is stationary 2 minutes

later.

a Draw a graph to show the cyclist’s motion.

b How far has the cyclist travelled?

01. 02. 03. 04.

30

05. 06.

60

O t( )h

v(km h-1)

01. 02. 01. 01. 01.

A BCDE

50 50 30 30

5 10 15 20

2

4

6

8

velocity m s()¡-1

O time s()

10

-20

20

40

60

O

t( )h

velocity km h()-1

0101 .. 0202 .. 0303 .. 0404 .. 0505 .. 0606 .. 0707 ..

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_16\445CamAdd_16.cdr Monday, 7 April 2014 4:18:04 PM BRIAN