Mathematics · Oct / Nov 2025 · Paper 51 · Question 3
YMA01
As printed in the paper
The question as text
3. [In this question i and j are horizontal perpendicular unit vectors.] A particle P of mass 2 kg moves on a smooth horizontal surface under the action of two forces F1 and F2, where F1 = (–2i + 3j) N and F2 = (4i + 2j) N.
Read automatically from the paper; the printed page above is exact.
Show the answer and mark scheme
3(a)[3]
Resultant force
(
) (
)( )
= −
+
+
+
=
+
2
i
3
j
4
i
2
j
2
i
5
j
Correct use of
F
=
m
a
Acceleration
)(
)
(
=
i
+
2.5
j
ms−
2
(
)
3(b)[4]
v
=
3
i
−
4
j
+
3
a
(
)
(
)
v
=
3
i
−
4
j
+
3
i
+
2.5
j
Use of Pythagoras
(
)
=
2
+
2
=
6.95 ms−
1
v
6
3.5
3(c)[3]
Resultant force
(
(
)
(
)
)( )
=
2
+
b
i
+
5
+
c
j
N
Correct use of direction to
form equation in b and c
only
e.g 2
+
b
=
5
+
c
or 2
+ =
b
λ
and 5
+ =
c
λ
with
λ eliminated
b c
−=
3
*
3(d)[4]
Use magnitude of resultant
to form an equation in b and
c
(
)
2
(
)
2
200
=
2
+
b
+
5
+
c
Form an equation in b or c
only
ALT 1:
Use magnitude of resultant
to form equation in λ
=
λ
2
+
λ
2
200
Use either
λ
=
10 or
λ
= −
10
to find equations in b and c
2
+ =
+ =
b
10 and 5
c
10
Or 2
+ = −
+ = −
b
10 and 5
c
10
(
)
F
=
8
i
+
5
j
N
3
(
)
= −
−
F
12
i
15
j
N
3
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