| Exam Board | Edexcel |
|---|---|
| Module | M1 (Mechanics 1) |
| Year | 2016 |
| Session | January |
| Marks | 13 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Travel graphs |
| Type | Vertical motion under gravity |
| Difficulty | Moderate -0.3 This is a standard M1 kinematics question using SUVAT equations with straightforward application of v² = u² + 2as for part (a), v = u + at for part (b), and routine sketching for part (c). While it requires multiple steps and careful tracking of signs/directions, it involves no novel problem-solving—just systematic application of well-practiced techniques to a textbook projectile motion scenario. |
| Spec | 3.02b Kinematic graphs: displacement-time and velocity-time3.02d Constant acceleration: SUVAT formulae3.02h Motion under gravity: vector form |
| Answer | Marks |
|---|---|
| 4(b) | First M1 for a complete method to find an intermediate time (A to top or A to O) |
| Answer | Marks |
|---|---|
| 4(c) | First B1 for a SINGLE straight line (N.B. If they have a continuous vertical line as |
| Answer | Marks |
|---|---|
| (ii) | T T |
| Answer | Marks |
|---|---|
| 2 | M1 A1 |
| Answer | Marks |
|---|---|
| (b) | 9410x84 |
| Answer | Marks |
|---|---|
| 1x1.8 | M1 |
| Answer | Marks |
|---|---|
| (ii) | First M1 for a complete method to find an equation in T and x only. |
Question 4:
--- 4(b) ---
4(b) | First M1 for a complete method to find an intermediate time (A to top or A to O)
First A1 for a correct equation or equations.
Second A1 for any intermediate time (e.g. t = 8/ , t = 2/ , t = 18/ , t =
A TOP 7 A O 7 A O 7 A A
16/7)
Second dM1 for a complete method to find the total time.
Third A1 for 2.9 or 2.86 (s) No other final answers.
For a complete method which does not involve an intermediate time e.g find u
(=14) at O, then use u to find the whole time:
First dM1 dependent on 2nd M1, for finding u
First A1 for u = 14
Second M1 for: 0 = 14t – 1/2gt2 or -14 = 14 – gt
Second A1
Third A1 for t =2.86 or 2.9
--- 4(c) ---
4(c) | First B1 for a SINGLE straight line (N.B. If they have a continuous vertical line as
well, give B0), with –ve gradient, starting on +ve v-axis (at A say) and crossing
the t-axis. (at B say).
SC: A single str. line, with –ve gradient, which starts at (2/7, 11.2) (clearly
marked) can score a max B1B1B0B0.
Second dB1, dependent on first B1, for the line finishing at C say, with AB < BC if
no scale, or at v = V ,where V < -11.2 , if marked.
Third B1 (independent) for their (possibly first) line starting at (0,11.2)
Fourth B1 (independent) for 1.1(4) (allow 8/7 if over accuracy already penalised
elsewhere) marked correctly (line may not cross the axis and there may be more
than one line)
N.B. Line may be reflected in t-axis, with appropriate adjustments to marks.
5(a)
(i)
(ii) | T T
1 2
2.2 m
A G B
40 N 120 N
M(B), 4T 120 x 1.8 + 40(4x)
1
T 9410x
1
M(A), 4T 120 x 2.2 + 40x
2
T 6610x
2 | M1 A1
A1
M1 A1
A1 (6)
(b) | 9410x84
x1
6610x84
x1.8
1x1.8 | M1
M1
A1 both CV
A1 (4)
10
Notes
5(a)(i)
(ii) | First M1 for a complete method to find an equation in T and x only.
A
First A1 for a correct equation in T and x only.
A
Second A1 for 94 – 10x
Second M1 for a complete method to find an equation in T and x only.
B
First A1 for a correct equation in T and x only.
B
Second A1 for 66 + 10xA small stone is projected vertically upwards from the point $O$ and moves freely under gravity. The point $A$ is 3.6 m vertically above $O$. When the stone first reaches $A$, the stone is moving upwards with speed 11.2 m s$^{-1}$. The stone is modelled as a particle.
\begin{enumerate}[label=(\alph*)]
\item Find the maximum height above $O$ reached by the stone. [4]
\item Find the total time between the instant when the stone was projected from $O$ and the instant when it returns to $O$. [5]
\item Sketch a velocity-time graph to represent the motion of the stone from the instant when it passes through $A$ moving upwards to the instant when it returns to $O$. Show, on the axes, the coordinates of the points where your graph meets the axes. [4]
\end{enumerate}
\hfill \mbox{\textit{Edexcel M1 2016 Q4 [13]}}