CAIE A-Level Mathematics 4.5.5 Instantaneous acceleration

CAIE A-Level Mathematics 4.5.5 Instantaneous acceleration
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

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

How this is tested

  • 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

Question 3(b)

[Maximum number: 3]

A car of mass 800 kg is moving on a straight road.
When the car is moving at a constant speed of 20 ms−120 \mathrm{~ms}^{-1} on a horizontal section of the road, the engine of the car is working at P WP \mathrm{~W}.

When the car is moving at a constant speed of 12 ms−112 \mathrm{~ms}^{-1} up a section of the road inclined at sin⁡−10.15\sin ^{-1} 0.15 to the horizontal, the engine of the car is also working at P WP \mathrm{~W}.

On both sections of the road there is a constant force of magnitude R NR \mathrm{~N} resisting the motion of the car.

Find the acceleration of the car when it is moving at 10 ms−110 \mathrm{~ms}^{-1} up the inclined section of the road with the engine working at 32 kW .