| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2014 |
| Session | January |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Find acceleration from distances/times |
| Difficulty | Moderate -0.3 This is a standard two-part SUVAT problem requiring students to set up simultaneous equations from given distances and times. While it involves algebraic manipulation with two unknowns (initial speed and acceleration), the approach is routine for M1 students who have practiced similar checkpoint problems. The arithmetic is straightforward and no conceptual insight beyond applying s=ut+½at² twice is needed. |
| Spec | 3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| \(48 = 3u + \frac{1}{2} \cdot 9a\) | M1 A1 | M1 for equation in \(u\) and \(a\) only; A1 correct equation |
| \(248 = 8u + \frac{1}{2} \cdot 64a\) | M1 A1 | M1 for second equation in \(u\) and \(a\) only (M0 for \(200 = 5u + 0.5a \cdot 5^2\)); A1 correct equation |
| \(a = 6 \text{ ms}^{-1}\) | A1 | Third M1 independent for solving simultaneous equations; A1 for \(a=6\) |
| \(u = 7 \text{ ms}^{-1}\) | M1 A1 (7) | A1 for \(u=7\) |
| Answer | Marks |
|---|---|
| \(v = 48/3\) at \(t=1.5\) (must be used/stated) | M1 A1 |
| \(v = 200/5\) at \(t=5.5\) (must be used/stated) | M1 A1 |
| \(a = (40-16)/(5.5-1.5) = 6\) | DM1 A1 |
| \(u = 16 - (6 \times 1.5) = 7\) | A1 |
## Question 5:
$48 = 3u + \frac{1}{2} \cdot 9a$ | M1 A1 | M1 for equation in $u$ and $a$ only; A1 correct equation
$248 = 8u + \frac{1}{2} \cdot 64a$ | M1 A1 | M1 for second equation in $u$ and $a$ only (M0 for $200 = 5u + 0.5a \cdot 5^2$); A1 correct equation
$a = 6 \text{ ms}^{-1}$ | A1 | Third M1 independent for solving simultaneous equations; A1 for $a=6$
$u = 7 \text{ ms}^{-1}$ | M1 A1 (7) | A1 for $u=7$
**Alternative (average speed = actual speed at half-time):**
$v = 48/3$ at $t=1.5$ (must be used/stated) | M1 A1 |
$v = 200/5$ at $t=5.5$ (must be used/stated) | M1 A1 |
$a = (40-16)/(5.5-1.5) = 6$ | DM1 A1 |
$u = 16 - (6 \times 1.5) = 7$ | A1 |
---5. A racing car is moving along a straight horizontal track with constant acceleration. There are three checkpoints, $P , Q$ and $R$, on the track, where $P Q = 48 \mathrm {~m}$ and $Q R = 200 \mathrm {~m}$. The car takes 3 s to travel from $P$ to $Q$ and 5 s to travel from $Q$ to $R$. Find\\
(i) the acceleration of the car,\\
(ii) the speed of the car as it passes $P$.\\
\hfill \mbox{\textit{Edexcel M1 2014 Q5 [7]}}