CAIE A-Level Mathematics AS 4.5.5 Instantaneous Acceleration Questions

Practise relating changing engine power to instantaneous acceleration in mechanical systems.

Exam points

relate power, force, speed and instantaneous acceleration
calculate acceleration when engine power changes suddenly
analyse vehicles and connected systems with variable power and resistance

[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.

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

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CAIE A-Level Mathematics AS 4.5.5 Instantaneous Acceleration Questions question 1