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 1300 kg is moving on a straight road.

On a horizontal section of the road, the car has a constant speed of $30 \mathrm{~m} \mathrm{~s}^{-1}$ and there is a constant force of 650 N resisting the motion.

Given that this power is suddenly increased by 9 kW , find the instantaneous acceleration of the car.

their $19500+9000=D F \times 30$

B1FT

Oe FT their 19.5 in watts only.

D F-650=1300 a
Newton's second law horizontally;
3 relevant terms;
dimensionally correct but allow sign errors;
allow with
their driving force or just D F.

$a=\frac{3}{13}=0.231 \mathrm{~m} \mathrm{~s}^{-2}$
0.23076923...

Alternative scheme for 6(a)(ii)

$9000=D F \times 30$

*B1

oe e.g. $D F=\frac{9000}{30}$ .

D F=1300 a
Resolving horizontally using Newton's second law;
2
relevant terms;
dimensionally correct but allow sign
errors.

$a=\frac{3}{13}=0.231 \mathrm{~m} \mathrm{~s}^{-2}$
0.23076923...

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