CAIE A-Level Mathematics AS 4.4.3 Constant Acceleration Questions

Practise combining dynamics, friction and kinematics to solve multi-stage mechanics problems.

Exam points

combine Newton’s laws with kinematics in multi-stage motion
model friction, tension and resistance on slopes and connected systems
solve for times, speeds, distances and unknown forces in applications

[Maximum number: 4]

Figure for Question CAIE A-Level Mathematics AS 4.4.3 Constant Acceleration Questions question 1 — CAIE A-Level Mathematics AS

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.]

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

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CAIE A-Level Mathematics AS 4.4.3 Constant Acceleration Questions question 1