Mathematics · May / June 2022 · Paper 51 · Question 6
YMA01
As printed in the paper
The question as text
6. A particle P is moving with constant acceleration. At time t = 1 second, P has velocity (–i + 4j) m s–1 At time t = 4 seconds, P has velocity (5i – 8j) m s–1 Find the speed of P at time t = 3.5 seconds. (6)
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i
j
i
j
j
v
= −+
(
i
4 )
j
+
2.5(2
i
−
4 )
j
=
(4
−
6 )
v
i
52
=
7.2 (m s ) or better
−
1
Speed =
4
2
+ −
( 6)
2
=
[
]
[
]
(4 3.5)
−
−−+
(
4 ) =(3.5 1) (5
−
−
8 )
−
OR:
v
i
j
i
j
v oe
j
=
(4
−
6 )
v
i
52
=
7.2 (m s ) or better
−
1
Speed =
4
2
+ −
( 6)
2
=
Notes for question 6
M1 For use of
v
=
u a , with t = 3 oe, to give an equation in a only
+
t
Allow u and v reversed
A1 Correct unsimplified equation in a only
M1 For an equation in v only using their a and t = 2.5 oe (e.g. they may
find u (=( 3
j ), the velocity at t = 0, then use t = 3.5)
−
i
+
8 )
M0 if they assume u = 0
A1 (4
j
−
6 )
i
M1 Use of Pythagoras, including square root, to find magnitude of their
v
A1 cao
OR: Ratio method
M2 for an equation in v only, with the correct structure
A1 Correct unsimplified ratio equation
A1 (4
j
i
−
6 )
M1 Use of Pythagoras, including square root, to find magnitude of their
v
A1 cao
speed
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