| Exam Board | CAIE |
|---|---|
| Module | FP2 (Further Pure Mathematics 2) |
| Year | 2019 |
| Session | June |
| Marks | 4 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Circular Motion 1 |
| Type | Radial and transverse acceleration |
| Difficulty | Moderate -0.3 This is a straightforward application of standard circular motion formulas. Students need to differentiate θ = 1 - cos(2t) twice to find angular velocity and acceleration, then substitute into the radial (rω²) and transverse (rα) acceleration formulas. The calculation is routine with no conceptual challenges beyond recalling the standard results, making it slightly easier than average for Further Maths. |
| Spec | 6.05e Radial/tangential acceleration |
| Answer | Marks | Guidance |
|---|---|---|
| 1(i) | a = 2 (dθ /dt)2 = 2 (2 sin 2t)2 = 2 (2 sin π/3) 2 | |
| R | M1 | Verify radial acceleration a at t = π/6 from rω2 |
| Answer | Marks |
|---|---|
| = 2 (√3) 2 = 6 [m s-2] AG | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| 1(ii) | a = 2 d2θ /dt2 = 2 (4 cos 2t) = 2 (4 cos π/3) | |
| T | M1 | Find transverse acceleration a at t = π/6 by differentiation |
| Answer | Marks |
|---|---|
| = 4 [m s-2] | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Question | Answer | Marks |
Question 1:
--- 1(i) ---
1(i) | a = 2 (dθ /dt)2 = 2 (2 sin 2t)2 = 2 (2 sin π/3) 2
R | M1 | Verify radial acceleration a at t = π/6 from rω2
R
= 2 (√3) 2 = 6 [m s-2] AG | A1
2
--- 1(ii) ---
1(ii) | a = 2 d2θ /dt2 = 2 (4 cos 2t) = 2 (4 cos π/3)
T | M1 | Find transverse acceleration a at t = π/6 by differentiation
T
= 4 [m s-2] | A1
2
Question | Answer | Marks | GuidanceA particle $P$ moves along an arc of a circle with centre $O$ and radius 2 m. At time $t$ seconds, the angle $POA$ is $\theta$, where $\theta = 1 - \cos 2t$, and $A$ is a fixed point on the arc of the circle.
(i) Show that the magnitude of the radial component of the acceleration of $P$ when $t = \frac{1}{6}\pi$ is 6 m s$^{-2}$. [2]
(ii) Find the magnitude of the transverse component of the acceleration of $P$ when $t = \frac{1}{6}\pi$. [2]
\hfill \mbox{\textit{CAIE FP2 2019 Q1 [4]}}