This test is split into two sections. Section A covers Dynamics. Section B covers Thermodynamics.
Candidates should answer all parts in both Sections. Each Section is worth 50 marks.
Time allowed: 2 hours.
Only calculators that confirm to the list of models approved by the School of Engineering may
be used in this examination. The Engineering Data Book and Thermodynamic Tables will be
provided.
Read carefully the instructions on the answer booklets and ensure the details required are written
on every booklet submitted.
1. Answer all parts. The following formulae for normal and tangential velocity and acceleration
in ℝ2 may be helpful for this Section:
Velocity 𝐯 = 𝑠̇ 𝐞𝒕
Acceleration 𝐚 = 𝑣̇ 𝐞𝒕 + (𝑣 2 ⁄𝜌)𝐞𝒏
where 𝐞𝒕 and 𝐞𝒏 are the unit tangential and normal vectors, respectively, and 𝜌 is the radius of
curvature.
(a) The position of a particle moving along a straight line is given by
𝑥 = (𝑡 3 − 13.5𝑡 2 + 22.5𝑡) m, where 𝑡 is in seconds. Determine the position of the
particle when 𝑡 = 5 s and the total distance it travels during the 5 second time interval.
Hint: Plot the path to determine the total distance travelled.
(14 marks)
(b) The automobile in Figure 1b is originally at rest when (arclength) 𝑠 = 0. If its speed then
increases according to 𝑣̇ = (0.06𝑡 2 ) ms–2, where 𝑡 is in seconds, determine the
magnitudes of its velocity and acceleration at 𝑠 = 120 𝑚. Hint: The automobile will be
on the curved path so use normal and tangential components.
(14 marks)
Figure 1b
Question 1 continues overleaf
2
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