Mathematics · May / June 2023 · Paper 51 · Question 5
YMA01
As printed in the paper
The question as text
5. speed –1) (m s V time (s) 0 30 T Figure 2 The speed-time graph in Figure 2 illustrates the motion of a car travelling along a straight horizontal road. At time t = 0 , the car starts from rest and accelerates uniformly for 30 s until it reaches a –1 speed of V m s –1 until time t = T seconds. The car then travels at a constant speed of V m s
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
5(a)[2]
T
+
T
−
30
V
For car:
2
(
)
(metres) * Allow (
)
V T −
15
T
−
15
V
5(b)[2]
The answer is a drawing: see the picture of this mark scheme row.
5(c)[2]
speed
V
=
40
30
4
V
(
speed
)
(
m s−)*
1
=
3
5(d)[5]
For motorbike
1 4
V
4
V
1 4
V
(
)
OR:
×
40
+
×
10
+
+
V
T
−
60
2
3
3
2
3
OR:
1
4
V
4
V
1
4
V
(
)
×
40
+
×
10
+
−
V
T
−
60
+
V T
(
−
60)
2
3
3
2
3
1
4
V
1
4
V
OR:
(10
50)
(
60
)
×
×
+
+
+
V
T
−
2
3
2
3
(Simplified: 7
VT
−
30
V
)
6
Equate their motorbike distance to (
)
V T −
15
to give an equation in T only
90
T =
ALT: Find area of upper trapezium and parallelogram
(differences in areas)
1
V
(
)
T
−
40 10
+
2
3
and 10V
Equate to give an equation in T only (V cancels)
T =
90
Notes for Question 5
(a)
M1
Uses total area under graph to find an expression for the distance in terms of V and T
only
May use:
30
T
+
T
−
Trapezium:
V
2
1 30
(
)
(
30
)
triangle + rectangle :
V
+
V T
−
2
1 (30
a triangle subtracted from a rectangle:
VT
−
×
V
)
2
1 30
OR use of suvat: (
)
(
30
)
V
+
V T
−
2
A1*
Given answer correctly obtained (allow omission of ‘metres’.
(b)
N.B. If graph is not done on either of the given graphs on the question paper, they score
B0B0 .
B1
Correct shape with acceleration lines parallel and meeting at (T, V)
B0 if continuous vertical line at t = T
B1
Correct horizontal labels. Accept appropriately labelled delineators.
N.B. This mark is independent of the first B1.
(c)
M1
Correct method using gradients or suvat to obtain an equation in V only
A1*
Given answer correctly obtained
(d)
M1
For motorbike: find an expression for the TOTAL area under the graph (or use suvat) to
find the total distance travelled in terms of V and T only.
1
4
V
4
V
1
4
V
(
)
N.B.
×
40
+
×
10
+
−
V
T
−
60
is M0 as it omits a part of the area.
2
3
3
2
3
A1
Correct unsimplified expression with at most one error/slip
A1
Correct unsimplified expression
M1
Clear attempt to equate their distance to the given distance in part (a) to give an equation
in T only i.e. the V’s must cancel but they do not need to be cancelled for this mark.
N.B. This is an independent mark.
A1
cao
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