| Exam Board | CAIE |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2022 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Distance in nth second |
| Difficulty | Standard +0.3 This is a standard SUVAT problem requiring students to set up two equations from 'distance in nth second' and solve simultaneously for initial velocity and acceleration. While it involves algebraic manipulation and understanding of the nth second formula, it's a routine mechanics exercise with a clear method that students practice extensively in M1. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(52 = u(2) + 0.5a(2)^2 - \left(u(1) + 0.5a(1)^2\right)\) or \(64 = u(4) + 0.5a(4)^2 - (u(3) + 0.5a(3)^2)\) | M1 | Use of \(s = ut + \frac{1}{2}at^2\) or equivalent to form equation for 2nd or 4th second |
| M1 | Second equation in \(u\) and \(a\) | |
| \(52 = u + 1.5a\) and \(64 = u + 3.5a\) | A1 | Two correct equations in \(u\) and \(a\) |
| \(12 = 2a\) leading to \(a = 6\) | M1 | Solves simultaneous equations to find either \(u\) or \(a\) |
| Initial speed \(= 43\) ms\(^{-1}\) and acceleration \(= 6\) ms\(^{-2}\) | A1 |
| Answer | Marks | Guidance |
|---|---|---|
| Answer | Mark | Guidance |
| \(s = 43\times10 + 0.5\times6\times10^2\) | M1 | Use of \(s = ut + \frac{1}{2}at^2\) or equivalent |
| Distance \(= 730\) m | A1 FT | FT \(10u + 50a\) with \(u\) and \(a\) from part (a) |
## Question 4(a):
| Answer | Mark | Guidance |
|--------|------|----------|
| $52 = u(2) + 0.5a(2)^2 - \left(u(1) + 0.5a(1)^2\right)$ or $64 = u(4) + 0.5a(4)^2 - (u(3) + 0.5a(3)^2)$ | M1 | Use of $s = ut + \frac{1}{2}at^2$ or equivalent to form equation for 2nd or 4th second |
| | M1 | Second equation in $u$ and $a$ |
| $52 = u + 1.5a$ and $64 = u + 3.5a$ | A1 | Two correct equations in $u$ and $a$ |
| $12 = 2a$ leading to $a = 6$ | M1 | Solves simultaneous equations to find either $u$ or $a$ |
| Initial speed $= 43$ ms$^{-1}$ and acceleration $= 6$ ms$^{-2}$ | A1 | |
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## Question 4(b):
| Answer | Mark | Guidance |
|--------|------|----------|
| $s = 43\times10 + 0.5\times6\times10^2$ | M1 | Use of $s = ut + \frac{1}{2}at^2$ or equivalent |
| Distance $= 730$ m | A1 FT | FT $10u + 50a$ with $u$ and $a$ from part (a) |
---4 A particle $P$ travels in the positive direction along a straight line with constant acceleration. $P$ travels a distance of 52 m during the 2 nd second of its motion and a distance of 64 m during the 4th second of its motion.
\begin{enumerate}[label=(\alph*)]
\item Find the initial speed and the acceleration of $P$.
\item Find the distance travelled by $P$ during the first 10 seconds of its motion.
\end{enumerate}
\hfill \mbox{\textit{CAIE M1 2022 Q4 [7]}}