CAIE A-Level Mathematics 4.5.5 Instantaneous acceleration

Practise instantaneous acceleration questions where changing engine power alters the driving force at a specified speed.

Exam points

convert changed power into driving force using P=Fv at the stated instant
apply Newton's second law with resistance and hill components to find acceleration
for linked car-and-caravan systems, use the common acceleration to find tension

[Maximum number: 3]

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

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

Given that this power is suddenly increased by 12 kW , find the instantaneous acceleration of the car.

$\mathrm{DF}=\frac{57000}{36}[=1583.3 .$ .
M1
Use changed Power in $P=\mathrm{DF} \times v$ .
$\frac{57000}{36}-1250=1400 a$
M1
For using Newton's 2nd law applied to the car.
$a=0.238 \mathrm{~ms}^{-2}$
A1

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4.5.5—Instantaneous acceleration question 1