Mathematics · Oct / Nov 2023 · Paper 51 · Question 2
YMA01
As printed in the paper
The question as text
2. acceleration –2) (m s 1.2 O time (s) 4 10 20 – 0.5 Figure 2 Two fixed points, A and B, are on a straight horizontal road. The acceleration-time graph in Figure 2 represents the motion of a car travelling along the road as it moves from A to B. At time t = 0, the car passes through A with speed 8 m s –1 At time t = 20 s, the car passes through B with speed v m s –1
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
2(a)[3]
v
u
at
(the value of w may not be seen)
:
(1.2)(10)
v
=
u
+
at
v
=
w
+
v =
18
*
2(b)[3]
Clear attempt to find distance using the area under their graph
2(c)[4]
from t = 0 to t = 20 or another suitable method, even if they
are using the wrong shapes.
Distance = (8
+
"6")
×
4
("6" 18) 10
+
×
+
(6 "6")
×
+
2
2
1
1
(6 4)
4 (8
6)
(6 6)
(6 10)
10 (18
6)
OR =
×
+
××
−
+
×
+
×
+
×
×
−
2
2
= 184 (m)
Notes for question 2
(a)
Complete method for finding the velocity (w) when t = 4 M0 if u = 0.
M1
N.B. 6 on its own can imply this mark.
Method completed to show the speed when t = 20 M0 if initial speed is not w.
M1
Fully correct solution leading to given answer
A1*
(b)
Correct shape of graph
B1
B1
Correct time labels
Correct speed labels
B1
N.B. Solid vertical line(s) B0 for the shape.
(c)
Complete method to find distance travelled in 20 seconds. May use speedtime
M1
graph or suvat equations for three sections (28m, 36m, 120m) of the journey.
Award this mark for a clear attempt to find the area and penalise errors in the A
marks. M0 if graph does not have three sections.
A1ft
Equation with at most one error, ft their “6”
Correct equation, ft their “6”
A1ft
A1
Correct final answer
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