Cambridge Additional Mathematics

Applications of differential calculus (Chapter 14) 381 VELOCITY Theaverage velocityof an object moving in a straight line in the ...

382 Applications of differential calculus (Chapter 14) Example 13 Self Tutor A particle moves in a straight line with displaceme ...

Applications of differential calculus (Chapter 14) 383 3 A particle moves in a straight line with velocity function v(t)=2 p t+3 ...

MOTION DEMO Be careful not to confuse speed with displacement. St st () () 384 Applications of differential calculus (Chapter 14 ...

The motion is actually , not above it as shown. on the line -1 0 1 origin position t=2 2 3 t=0 Since , the stationary point at i ...

When finding the total distance travelled, always look for direction reversals first. 386 Applications of differential calculus ...

s(t) O t Applications of differential calculus (Chapter 14) 387 5 A particle P moves in a straight line with displacement functi ...

There are countless examples in the real world where quantities vary with time, or with respect to some other variable. For exam ...

GRAPHING PACKAGE Applications of differential calculus (Chapter 14) 389 c dA dt =^16 t ¡^12 ) d^2 A dt^2 =¡ 121 t ¡^32 =¡ 1 12 t ...

150 151 C(150) chord C(151) ()canswer tangent ()banswer 1 390 Applications of differential calculus (Chapter 14) Example 16 Self ...

y x sea hill lake O Applications of differential calculus (Chapter 14) 391 6 A tank contains50 000litres of water. The tap is le ...

2 m xm piston μmust be in so the dimensions are correct. radians 12 cm A μ C B 10 cm P Q R 6 cm 7 cm μ y x P,(t t)cos sin t (1 0 ...

x=a x=p x=b _dy ^^ = 0 _dx _dy^^ = 0 dx_ y = f(x) Applications of differential calculus (Chapter 14) 393 There are many problems ...

0 x 20 A_'(x) xcm ycm xcm open DEMO + - 5 0 12.5 x d d__Vv~ 394 Applications of differential calculus (Chapter 14) Step 3: ...

DEMO 3 2 q A q B a b q B A 2 m 3 m 0° 90° 41.1° μ d d__L~ q 20 cm 10 cm 20 cm Applications of differential calculus (Chapt ...

hcm xcm GRAPHING PACKAGE 396 Applications of differential calculus (Chapter 14) Usecalculus techniquesto answer the following pr ...

hcm rcm μ B C 10 cm O lm xm 36 cm 36 cm C D B A y O x y=e-x² Applications of differential calculus (Chapter 14) 397 8 Infinitely ...

10 cm μμ end view q°^10 cm join A^10 cm C B sector ® 3 m 4 m μ 2 km Q PR 398 Applications of differential calculus (Chapter 14) ...

DEMO A xm B O 5 m ym wall A 1 xm B 1 O 5 m B 2 B 3 B 4 A 4 A 3 A 2 Applications of differential calculus (Chapter 14) 399 A 5 m ...

We must differentiate we substitute values for the particular case. Otherwise we will incorrectly treat the variables as constan ...