CAIE A-Level Mathematics 4.4.3 Constant-Acceleration Dynamics

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.

Exam points

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

[Maximum number: 4]

Figure for Question 4.4.3—Constant acceleration question 1 — CAIE A-Level Mathematics A2

Two particles A and B, of masses $3 m \mathrm{~kg}$ and $2 m \mathrm{~kg}$ respectively, are attached to the ends of a light inextensible string. The string passes over a fixed smooth pulley which is attached to the edge of a plane. The plane is inclined at an angle $\theta$ to the horizontal. A lies on the plane and B hangs vertically, 0.8 m above the floor, which is horizontal. The string between A and the pulley is parallel to a line of greatest slope of the plane (see diagram). Initially A and B are at rest.

When B reaches the floor it comes to rest.

Find the length of time after B reaches the floor for which A is moving up the plane. [You may assume that A does not reach the pulley.]

$v^{2}=0+2 \times 0.1 \times 0.8 \quad(v=0.4)$
M1
$-3 m g \sin 30-\mu \times 3 m g \cos 30=3 m a(a=-6.5)$
M1
0=-0.4-6.5 t
M1
$t=0.4 / 6.5=0.0615 \mathrm{~s}$
A1

All question bank results loaded

4.4.3—Constant acceleration question 1