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
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller user2895729. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $5.84. You're not tied to anything after your purchase.
