Cambridge Additional Mathematics

v(t)ms-1

t( )s

25

O

v(t) = ^^^^^^100______________

(t + 2) _ 2

502 Answers

c The particle is^43 m to the right of the origin, moving to the

right at^89 ms¡^1 , and accelerating at 272 ms¡^2.

9av(t)=

t^2

20

¡ 3 t+45ms¡^1

b

R 60

0 v(t)dt= 900. The train travels a total of^900 min

the first 60 seconds.

10 aShow thatv(t) = 100¡ 80 e

¡ 201 t

ms¡^1 and ast!1,

v(t)! 100 ms¡^1.

b 370 : 4 m

REVIEW SET 16A

1 A=

Rb

a[f(x)¡g(x)]dx+

Rc

b[g(x)¡f(x)]dx

+

Rd

c[f(x)¡g(x)]dx

2a2+¼ b¡ 2 c ¼

3 No, total area shaded=

R 1

¡ 1 f(x)dx¡

R 3

1 f(x)dx.

4 k=^3

p

16 54 : 5 units^2

6a

bThe particle moves in the positive direction initially, then at

t=2, 623 m from its starting point, it changes direction. It

changes direction again at t=4, 513 m from its starting

point, and att=5,itis 623 m from its starting point again.

c 623 m d 913 m

7 (3¡ln 4)units^282 : 35 m

REVIEW SET 16B

1av(t)=3t^2 ¡ 30 t+27cm s¡^1

b¡ 162 cm ( 162 cm to the left of the origin)

2a

c (1¡¼ 4 )units^2

3 a=ln3, b=ln5

4aa(t)=2¡ 6 tms¡^2 bs(t)=t^2 ¡t^3 +cm

c ¡ 4 m( 4 m to the left)

5 k=^436 m=¼ 3 7 (^4 ¼¡1)units^2

8av(0) = 25ms¡^1 , v(3) = 4ms¡^1

bast!1,v(t)! 0 from above

c

d 3 seconds ea(t)=¡^200

(t+2)^3

ms¡^2 , t> 0

f k=^15

24 t(seconds)

++-

0

v(t)

y=¡¡sinx

y = -Qw Qwcos_2x

x

y

¼

1

O

cyan magenta yellow black

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Y:\HAESE\CAM4037\CamAdd_AN\502CamAdd_AN.cdr Tuesday, 8 April 2014 8:40:48 AM BRIAN