A car of mass $$$1250 \mathrm{~kg}$$$ is moving on a straight road. On a section of the road inclined at $$$\sin ^{-1} 0.096$$$ to the horizontal, the resistance to the motion of the car is $$$(1000+8 v) \mathrm{N}$$$ when the speed of the car is $$$v \mathrm{~m} \mathrm{~s}^{-1}$$$. The car travels up this section of the road at constant speed with the engine working at $$$60 \mathrm{~kW}$$$. Find this constant speed. ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................ ........................................................................................................................................................

Mathematics

IGCSE&ALevel

CAIE

Exam No：9709_s20_qp_42 Year：2020 Question No：5(b)

Answer:

$D F=1000+8 v+1250 \times 10 \times 0.096$
$2200+8 v$
$60000=(2200+8 v) v$
$8 v^{2}+2200 v-60000=0$
$v=25$

Knowledge points:

4.1.3 use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of the components in any direction is zero （Solutions by resolving are usually expected, but equivalent methods (e.g. triangle of forces, Lami’s Theorem, where suitable) are also acceptable; these other methods are not required knowledge, and will not be referred to in questions.）

4.5.4 use the definition of power as the rate at which a force does work, and use the relationship between power, force and velocity for a force acting in the direction of motion Including calculation of (average) power;P = Fv

Answer:

Knowledge points:

Solution:

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