| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2013 |
| Session | June |
| Marks | 11 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Multi-stage motion with algebraic unknowns |
| Difficulty | Moderate -0.3 This is a standard M1 kinematics problem involving speed-time graphs and constant acceleration equations. Parts (a)-(b) require basic graph sketching and using area under graph equals distance. Parts (c)-(d) involve setting up simultaneous equations for two vehicles meeting, which is routine M1 material. All techniques are textbook exercises with no novel problem-solving required, making it slightly easier than average. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae |
| Answer | Marks | Guidance |
|---|---|---|
| Speed | Shape | B1 |
| Figures | B1 | |
| (2) |
| Answer | Marks |
|---|---|
| \(\frac{(120 + T)22}{2} = 2145\) | M1 A1 |
| \(T = 75\) | A1 |
| (3) |
| Answer | Marks |
|---|---|
| \(\frac{(t + I - 30)22}{2} = 990\) | M1 A1 |
| \(t = 60\) | A1 |
| Answer \(= 60 - 10 = 50\) | A1 |
| (4) |
| Answer | Marks |
|---|---|
| \(990 = 0.5a50^2\) | M1 |
| \(a = 0.79, 0.792, 99/125\) oe | A1 |
| (2) | |
| [11] |
## Part (a)
Speed | Shape | B1
Figures | B1
| (2)
## Part (b)
$\frac{(120 + T)22}{2} = 2145$ | M1 A1
$T = 75$ | A1
| (3)
## Part (c)
$\frac{(t + I - 30)22}{2} = 990$ | M1 A1
$t = 60$ | A1
Answer $= 60 - 10 = 50$ | A1
| (4)
## Part (d)
$990 = 0.5a50^2$ | M1
$a = 0.79, 0.792, 99/125$ oe | A1
| (2)
| [11]
**Notes for Question 5:**
**Q5(a)**
- First B1 for a trapezium starting at the origin and ending on the $t$-axis.
- Second B1 for the figures marked (allow missing 0 and a delineator oe for $T$) (allow if they have used $T = 75$ correctly on their graph)
**Q5(b)**
- First M1 for producing an equation in their $T$ only by equating the area of the trapezium to 2145, with the correct no. of terms. If using a single trapezium, we need to see evidence of using $\frac{1}{2}$ the sum of the two parallel sides or if using triangle(s), need to see $\frac{1}{2}$ base x height.
- Second A1 cao for a correct equation in $T$ (This is not f.t. on their $T$)
- Third A1 for $T = 75$.
- N.B. Use of a single suvar equation for the whole motion of the car e.g. $s = \frac{(u+v)}{2}$ is M0
**Q5(c)**
- First M1 for producing an equation in $t$ only (they may use $(t - 30)$ oe as their variable) by equating the area of the trapezium to 990, with the correct no. of terms. If using a trapezium, we need to see evidence of using $\frac{1}{2}$ the sum of the two parallel sides or if using triangle(s), need to see $\frac{1}{2}$ base x height.
- First A1 for a correct equation.
- Second A1 for $t = 60$ (Allow $30 + 30$).
- Third A1 for answer of 50.
- N.B. Use of a single suvar equation for the whole motion of the car e.g. $s = \frac{(u+v)}{2}$ is M0.
- Use of the motion of the motorcycle is M0 (insufficient information).
- Use of $v = 22$ for the motorcycle is M0.
**Q5(d)**
- First M1 for an equation in $a$ only.
- First A1 for $a = 0.79, 0.792, 99/125$ oe
- N.B. Use of $v = 22$ for the motorcycle is M0.
---A car is travelling along a straight horizontal road. The car takes 120 s to travel between two sets of traffic lights which are 2145 m apart. The car starts from rest at the first set of traffic lights and moves with constant acceleration for 30 s until its speed is $22 \text{ m s}^{-1}$. The car maintains this speed for $T$ seconds. The car then moves with constant deceleration, coming to rest at the second set of traffic lights.
\begin{enumerate}[label=(\alph*)]
\item Sketch, in the space below, a speed-time graph for the motion of the car between the two sets of traffic lights. [2]
\item Find the value of $T$. [3]
\end{enumerate}
A motorcycle leaves the first set of traffic lights 10 s after the car has left the first set of traffic lights. The motorcycle moves from rest with constant acceleration, $a \text{ m s}^{-2}$, and passes the car at the point $A$ which is 990 m from the first set of traffic lights. When the motorcycle passes the car, the car is moving with speed $22 \text{ m s}^{-1}$.
\begin{enumerate}[label=(\alph*)]
\setcounter{enumi}{2}
\item Find the time it takes for the motorcycle to move from the first set of traffic lights to the point $A$. [4]
\item Find the value of $a$. [2]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2013 Q5 [11]}}