BREAKING
Imaginary number feels seen, refuses to be real★Matrices multiplied in wrong order, student loses faith★Proof by induction ends, nobody knows why it worked★
  1. Home
  2. A Level
  3. Further Mathematics
  4. OCR
  5. Kinematics

OCR A Level Further Maths

Topic questions Mechanics Kinematics

Kinematics

5 questions · 59 marks · about 1 hour

Kinematics questions

TopicKinematics

OCR H245 Kinematics 5 questions

Pure Core 1 June 2025, Question 9 9 marks

A pendulum comprises an object P of mass m kg and a string of length 7 m. One end of the string is attached to P and the other end is attached to a fixed point A.

At time t seconds, t ⩾ 0, the string forms an angle of θ radians, measured anti-clockwise, from the downward vertical through A, as shown in the diagram.

When t = 0, θ = θ0 > 0 and P is released from rest. You may assume that in the subsequent motion P moves along the arc of a circle, centre A and radius 7 m, and that |θ| ⩽ θ0 for all t ⩾ 0.

Figure for question 9

The motion of P is modelled by the following differential equation.

Question 9, shown as an image

In some situations, it is appropriate to approximate (∗) with the following differential equation.

Question 9, shown as an image
(a)
Figure for question 9
[1]
Reveal mark scheme Mark scheme for question 9(a)
(b)
Figure for question 9
[6]
Reveal mark scheme Mark scheme for question 9(b)
(c)

An additional force now acts on P. It can be shown that it is now appropriate to model the motion of P with the differential equation fraction + fraction + fraction = 0 where k > 0.

Find the range of values of m, in terms of k, for which the motion of the pendulum is

overdamped.

[2]
Reveal mark scheme Mark scheme for question 9(c)

Pure Core 1 June 2024, Question 10 10 marks

Figure for question 10
(a)
Figure for question 10
[2]
Reveal mark scheme Mark scheme for question 10(a)
(b)

Using an integrating factor, determine the first time at which B is stationary according to the

model.

[8]
Reveal mark scheme Mark scheme for question 10(b)

Pure Core 1 June 2023, Question 7 11 marks

Figure for question 7
(a)

The engineer applies the equation “ F = ma ” to the model of the motion of P and derives the following differential equation.

Question 7, shown as an image
(a)(i)
Figure for question 7
[1]
Reveal mark scheme Mark scheme for question 7(a)(i)
(a)(ii)

When t = 0 the displacement of P is 6 m, and it is travelling towards O with a speed of 5 ms-1.

Without attempting to solve the differential equation, find the acceleration of P

when t = 0.

[2]
Reveal mark scheme Mark scheme for question 7(a)(ii)
(b)(i)
Figure for question 7
[1]
Reveal mark scheme Mark scheme for question 7(b)(i)
(b)(ii)
Figure for question 7
[1]
Reveal mark scheme Mark scheme for question 7(b)(ii)
(b)(iii)
Figure for question 7
[4]
Reveal mark scheme Mark scheme for question 7(b)(iii)
(c)(i)
Figure for question 7
[1]
Reveal mark scheme Mark scheme for question 7(c)(i)
(c)(ii)
Figure for question 7
[1]
Reveal mark scheme Mark scheme for question 7(c)(ii)

Pure Core 2 November 2021, Question 8 16 marks

Figure for question 8
(a)
Question 8, shown as an image
[3]
Reveal mark scheme Mark scheme for question 8(a)
(b)

Find an expression for v in terms of t for t ⩾ 0.

[5]
Reveal mark scheme Mark scheme for question 8(b)
(c)

By considering the behaviour of v as t becomes large explain why, according to the model, P ’s

speed must reach a maximum value for some t > 0.

[2]
Reveal mark scheme Mark scheme for question 8(c)
(d)

Determine the maximum speed considered in part (c).

[2]
Reveal mark scheme Mark scheme for question 8(d)
(e)

Determine the greatest value of t for which the model is valid.

[4]
Reveal mark scheme Mark scheme for question 8(e)

Pure Core 1 November 2020, Question 10 13 marks

Figure for question 10
(a)

Show that the motion of the particle can be modelled by the following differential equation.

Question 10, shown as an image
[2]
Reveal mark scheme Mark scheme for question 10(a)
(b)

Solve the differential equation in part (a), giving the particular solution for v in terms of t,

λ and μ.

[7]
Reveal mark scheme Mark scheme for question 10(b)
(c)
Figure for question 10
[2]
Reveal mark scheme Mark scheme for question 10(c)
(d)
Figure for question 10
[1]
Reveal mark scheme Mark scheme for question 10(d)
(e)

Without solving the differential equation in part (d), write down what will happen to the

velocity in the long term according to this refined model.

[1]
Reveal mark scheme Mark scheme for question 10(e)

Report a problem with a question on this page
What is wrong?

Goes to whoever maintains the question split. No account needed and nothing is published on this page.

Memes

Certified Further Maths memes. Peer-reviewed by nobody.

Laugh now. Cry in the exam hall later. Then come back and do a past paper.

Prove it by induction
Write ‘clearly’ and move on
Me on the final ‘show that’
Using the formula booklet
Proving it by induction
Writing ‘by symmetry’ to skip half the work
Writing ‘trivially’ and daring the examiner
Further enlightenment, ranked

Mum 💖

how's further maths going?? 🥰

my answers are all complex rn

keep it simple love 💖

📱 Screen time this week · Spotify4h 59m

The answer was i. Nobody knows why

Further Maths starter pack

Calculator that does matricesProof that’s 3 pages longArgand diagram doodlesThis website
Collect all four. Prove it.