CAIE A-Level Mathematics 4.4.3 Constant-Acceleration Dynamics

CAIE A-Level Mathematics 4.4.3 Constant-Acceleration Dynamics
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise deriving a particle's constant acceleration from resolved forces and then applying suvat with consistent signs across motion on rough planes or successive stages.

How this is tested

  • resolve the forces along the motion and use their signed resultant to calculate acceleration
  • apply a suvat equation after deriving acceleration, keeping the chosen positive direction consistent
  • restart the model when a string breaks or motion reverses and change friction direction if required

Question 5

[Maximum number: 8]

A straight slope of length 60 m is inclined at an angle of 12∘12^{\circ} to the horizontal. A bobsled starts at the top of the slope with a speed of 5 ms−15 \mathrm{~ms}^{-1}. The bobsled slides directly down the slope.

Question 5(a)

(a)

It is given that there is no resistance to the bobsled's motion.

Find its speed when it reaches the bottom of the slope.

[ 3 ]

Question 5(b)

(b)

It is given instead that the coefficient of friction between the bobsled and the slope is 0.03 .

Find the time that it takes for the bobsled to reach the bottom of the slope.

[ 5 ]