CAIE A-Level Mathematics AS 4.5.4 Complex Loci Questions

Practise calculating engine and cyclist power from force, resistance and speed in mechanical motion.

Exam points

calculate power from force and velocity
find steady speeds and engine power against resistance
apply power equations to vehicles and mechanical systems

[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 ]

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

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CAIE A-Level Mathematics AS 4.5.4 Complex Loci Questions question 1

Question (a)

Question (i)

Question (b)