Cambridge Additional Mathematics

Vectors (Chapter 11) 299

If an object has initial position vectoraand

moves with constant velocityb, its position at

timetis given by

r=a+tb for t> 0.

Thespeedof the object is jbj.

Example 14 Self Tutor

μ

x

y

¶

=

μ

1

9

¶

+t

μ

3

¡ 4

¶

is the vector equation of the path of an object.

The timetis in seconds, t> 0. The distance units are metres.

a Find the object’s initial position.

b Plot the path of the object for t=0, 1 , 2 , 3.

c Find the velocity vector of the object. d Find the object’s speed.

e If the object continues in the same direction but increases its speed to 30 ms¡^1 ,

state its new velocity vector.

a At t=0,

μ

x

y

¶

=

μ

1

9

¶

) the object is at (1,9).

b

c The velocity vector is

μ

3

¡ 4

¶

.

d The speed is

̄

̄

̄

̄

μ

3

¡ 4

¶ ̄

̄

̄

̄=

p

32 +(¡4)^2

=5ms¡^1.

e Previously, the speed was 5 ms¡^1 and the velocity vector was

μ

3

¡ 4

¶

.

) the new velocity vector is 6

μ

3

¡ 4

¶

=

μ

18

¡ 24

¶

.

DEMO

Velocity is a vector.

Speed is a scalar.

O

A

R

b

a

r

y

x

t=0

(1 9),

5

5

O

t=1

(4 5),

t=2

(7 1),

t=3

(10 -3),

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_11\299CamAdd_11.cdr Friday, 4 April 2014 2:29:02 PM BRIAN