CAIE A-Level Mathematics 4.5.4 Complex loci

Practise power problems in mechanics, using P=Fv with resistance, constant speed, hills and engine output in Paper 4 contexts.

Exam points

use P=Fv to find driving force, power or speed from a given engine output
at constant speed, balance driving force with resistance and weight components on hills

[Maximum number: 4]

A car of mass 1400 kg is moving on a straight road against a constant force of 1250 N resisting the motion.

(a)

The car moves along a horizontal section of the road at a constant speed of $36 \mathrm{~m} \mathrm{~s}^{-1}$ .

[ 2 ]

(i)

Calculate, in kW , the power developed by the engine of the car.

[ 2 ]

Power $=1250 \times 36$ or $\mathrm{P}=\frac{360000}{8}[=45000 \mathrm{~J}]$
B1 FT
FT Work Done from $\frac{\mathbf{a}(\mathbf{i})}{8}$ .
$=45 \mathrm{~kW}$
B1

(b)

The car now travels at a constant speed of $32 \mathrm{~m} \mathrm{~s}^{-1}$ up a section of the road inclined at $\theta^{\circ}$ to the horizontal, with the engine working at 64 kW .

Find the value of $\theta$ .

[ 2 ]

$\frac{64000}{32}=1250+1400 g \sin \theta$
M1
For using DF= resistance + component of the weight of
the car.
$\theta=3.1[3.0708 \ldots]$
A1

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4.5.4—Complex loci question 1

Question (a)

Question (i)

Question (b)