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SOLID MECHANICS DYNAMICS PRE-REQUISITE STUDIES TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION This tutorial is essential for anyone studying the group of tutorials on beams. • Essential pre-requisite knowledge for Edexcel HNC Mechanical Principles UNIT 21722P. • Essential pre-requisite knowledge for the Engineering Council Diploma Exams D209 Mechanics of Solids and D225 Dynamics of Mechanical Systems. • Essential pre-requisite knowledge for the Engineering Council Certificate Exam C105 Mechanical and Structural engineering. • Covers part of the syllabus for the Engineering Council Certificate Exam C103 Engineering Science. On completion of this tutorial you should be able to • Define linear motion. •
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Figure 3 Average velocity = total distance travelled/time taken Average velocity = area under graph/base length Since the base length is also the time taken it follows that the area under the graph is the distance travelled. This is true what ever the shape of the graph. When working out the areas, the true scales on the graphs axis are used. WORKED EXAMPLE No.2 Find the average velocity and distance travelled for the journey depicted on the graph above. Also find the acceleration over the first part of the journey. SOLUTION Total Area under graph = A + B + C Area A = 5x7/2 = 17.5 (Triangle) Area B = 5 x 12 = 60 (Rectangle) Area C = 5x4/2 = 10 (Triangle) Total area = 17.5 + 60 + 10 = 87.5 The units resulting for the area are m/s x s = m Distance travelled = 87.5 m Time taken = 23 s Average velocity = 87.5/23 = 3.8 m/s Acceleration over part A = change in velocity/time taken = 5/7 = 0.714 m/s2. © D.J.DUNN 5 SELF ASSESSMENT EXERCISE No.2 1. A vehicle travelling at 1.5 m/s suddenly accelerates uniformly to 5 m/s in 30 seconds. Calculate the acceleration, the average velocity and distance travelled. (Answers 0.117 m/s2, 3.25 m/s and 97.5 m) 2. A train travelling at 60 km/h decelerates uniformly to rest at a rate of 2 m/s2. Calculate the time and distance taken to stop. (Answers 8.33 s and 69.44 m) 3. A shell fired in a gun accelerates in the barrel over a length of 1.5 m to the exit velocity
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