Mathematics · May / June 2022 · Paper 51 · Question 7
YMA01
As printed in the paper
The question as text
7. Two small children, Ajaz and Beth, are running a 100 m race along a straight horizontal track. They both start from rest, leaving the start line at the same time. Ajaz accelerates at 0.8 m s–2 up to a speed of 4 m s–1 and then maintains this speed until he crosses the finish line. Beth accelerates at 1 m s–2 for T seconds and then maintains a constant speed until she crosses the finish line. Ajaz and Beth cross the finish line at the same time.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
7(a)[3]
4 A
B
0 time
0 T t
4
5 (s)
7(b)[4]
0.8 =
(
t
+ −
t
5)
1
100
=
× OR
4
100
=
××+
5 4
4(
−
5)
t
2
2
t = 27.5 (s)
(27.5
27.5
)
1
+
−
T
OR
7(c)[4]
100
=
×
T
100
=
2 T
×
×
T
+
T
(27.5
−
T
)
2
oe
T
2
−
55
T
+
200
=
0
T = 3.915047… accept 3.9 or better
7(d)[2]
4
−
3.915..
0.085 or better (
m s−)
1
Notes for question 7
7(a)
B1 Correct shape for A’s graph.
B1 Correct shape for B’s graph with steeper gradient initially and must
cross A’s graph. Both graphs must end at the same time.
B0 once if solid vertical line at the end
B1 4 and T correctly marked. Allow appropriate delineators.
N.B. If graphs are on separate axes can score max B1B0B1
If no labels, give BOD. If incorrect labels, max B1B0B1
B1 5 (s) seen – could be on graph
7(b)
M1 Attempt at equation in t only, with correct structure
i.e. trapezium or (rectangle + triangle) or (rectangle – triangle) oe
including 1
where appropriate, based on total area (OR distance using
2
2 or more suvat formulae) being 100
M0 for a single suvat equation for the whole motion.
N.B. If they clearly use T (for t) in their equation and in their answer,
it’s M0 but give BOD where possible.
A1ft Correct equation in t only, ft on their 5
A1 cao
M1 Attempt at equation in T only, with correct structure,
i.e. trapezium or (rectangle + triangle) or (rectangle – triangle) oe based
7(c)
on total area (OR distance using 2 or more suvat formulae) being 100
M0 for a single suvat equation for the whole motion.
A1ft Correct equation in T only, ft on their 27.5
A1 Correct 3 term quadratic
A1 cao
M1 for 4 T
−
. (Allow
T −
4
)
7(d)
A1 ft follow through on their T value provided it’s < 4.
Must be correct to at least 2 SF.
Allow column vectors throughout except for the answer to (b).
Use trig to get an equation in a relevant angle e.g tanα= 1 or uses
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