| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Marks | 12 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Constant acceleration (SUVAT) |
| Type | Multi-phase journey: find unknown speed or time |
| Difficulty | Standard +0.3 This is a standard three-stage SUVAT problem requiring a speed-time graph sketch, application of v = u + at for two decelerations, and using area under the graph equals distance. While multi-step, it follows a routine M1 template with straightforward algebra and no conceptual surprises, making it slightly easier than average. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02c Interpret kinematic graphs: gradient and area3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| (a) [Speed-time graph showing constant speed \(5U\) from \(t=0\) to \(t=6\), constant speed \(2U\) from \(t=6\) to \(t=22\), and \(t=24\)] | B2 | |
| (b) using \(v = u + at\) with \(v = 2U, u = 5U, t = 6\) gives \(1^{\text{st}}\) decel. \(= -\frac{1}{2}U \text{ ms}^{-2}\) | M1 A1 | |
| using \(v = u + at\) with \(v = 0, u = 2U, t = 2\) gives \(2^{\text{nd}}\) decel. \(= U \text{ ms}^{-2}\) | M1 A1 | |
| (c) area under graph dist. travelled \(= 220\) m | M1 | |
| \(\frac{1}{2}(6)(3U) + 22(2U) + \frac{1}{2}(2)(2U) = 220\) | M1 A2 | |
| \(55U = 220\) \(\therefore U = 4 \text{ ms}^{-1}\) | M1 A1 | (12) |
**(a)** [Speed-time graph showing constant speed $5U$ from $t=0$ to $t=6$, constant speed $2U$ from $t=6$ to $t=22$, and $t=24$] | B2 |
**(b)** using $v = u + at$ with $v = 2U, u = 5U, t = 6$ gives $1^{\text{st}}$ decel. $= -\frac{1}{2}U \text{ ms}^{-2}$ | M1 A1 |
using $v = u + at$ with $v = 0, u = 2U, t = 2$ gives $2^{\text{nd}}$ decel. $= U \text{ ms}^{-2}$ | M1 A1 |
**(c)** area under graph dist. travelled $= 220$ m | M1 |
$\frac{1}{2}(6)(3U) + 22(2U) + \frac{1}{2}(2)(2U) = 220$ | M1 A2 |
$55U = 220$ $\therefore U = 4 \text{ ms}^{-1}$ | M1 A1 | (12)6. A particle moving in a straight line with speed $5 U \mathrm {~m} \mathrm {~s} ^ { - 1 }$ undergoes a uniform deceleration for 6 seconds which reduces its speed to $2 \mathrm { Um } \mathrm { s } ^ { - 1 }$. It maintains this speed for 16 seconds before uniformly decelerating to rest in a further 2 seconds.
\begin{enumerate}[label=(\alph*)]
\item Sketch a speed-time graph displaying this information.
\item Find an expression for each of the decelerations in terms of $U$.
Given that the total distance travelled by the particle during this period of motion is 220 m ,
\item find the value of $U$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 Q6 [12]}}