Activity 3: A vehicle accelerates from rest, and its speed is approximated by the following function: v(t) = 0.1 t e 30/ Ve2+50 meters/second, where t is in seconds (a) Determine the travelled distance after 80 seconds by using Mid-ordinate Rule, Trapezoidal Rule, and Simpson's Rule, once with 5 intervals, and once with 10 intervals. Show all steps by hand for full consideration of the work. (b) Formulate a mathematical model on MATLAB to calculate a nearly exact value of the travelled distance after 80 seconds. (c) Compare between your findings in terms of applicability, accuracy, and speed. Explain. (d) Formulate a mathematical model on MATLAB to calculate the travelled distance at any time between 10 and 80 seconds (with a time step of 1 second). Plot the travelled distance versus time then use curve fitting to obtain an approximate formula of travelled distance as a function of time. HT Page 4 of 4 Al Hussein Technical Learning Outcomes and Assessment Criteria Learning Pass Merit Distinction Outcome LO2 Solve P4 Calculate the determinant of a set M2 Determine the D2 Validate systems of linear of given linear equations using a 3x3 solution to a set of given solutions for the equations relevant matrix engineering linear given engineering to engineering equations using the linear equations P5 Solve a system of three linear applications using Inverse Matrix Method matrix methods using appropriate equations using Gaussian elimination for a 3x3 matrix computer software LO3 Approximate P6 Estimate solutions of sketched M3 Solve engineering D3 Critically solutions of functions using a graphical problems and formulate evaluate the use contextualised estimation method mathematical models of numerical examples with P7 Calculate the roots of an equation using graphical and estimation graphical and numerical integration methods, using two different iterative numerical commenting on techniques methods their applicability P8 Determine the numerical integral and the accuracy of engineering functions using two of the methods different methods Activity 3: A vehicle accelerates from rest, and its speed is approximated by the following function: v(t) = 0.1 t e 30/ Ve2+50 meters/second, where t is in seconds (a) Determine the travelled distance after 80 seconds by using Mid-ordinate Rule, Trapezoidal Rule, and Simpson's Rule, once with 5 intervals, and once with 10 intervals. Show all steps by hand for full consideration of the work. (b) Formulate a mathematical model on MATLAB to calculate a nearly exact value of the travelled distance after 80 seconds. (c) Compare between your findings in terms of applicability, accuracy, and speed. Explain. (d) Formulate a mathematical model on MATLAB to calculate the travelled distance at any time between 10 and 80 seconds (with a time step of 1 second). Plot the travelled distance versus time then use curve fitting to obtain an approximate formula of travelled distance as a function of time. HT Page 4 of 4 Al Hussein Technical Learning Outcomes and Assessment Criteria Learning Pass Merit Distinction Outcome LO2 Solve P4 Calculate the determinant of a set M2 Determine the D2 Validate systems of linear of given linear equations using a 3x3 solution to a set of given solutions for the equations relevant matrix engineering linear given engineering to engineering equations using the linear equations P5 Solve a system of three linear applications using Inverse Matrix Method matrix methods using appropriate equations using Gaussian elimination for a 3x3 matrix computer software LO3 Approximate P6 Estimate solutions of sketched M3 Solve engineering D3 Critically solutions of functions using a graphical problems and formulate evaluate the use contextualised estimation method mathematical models of numerical examples with P7 Calculate the roots of an equation using graphical and estimation graphical and numerical integration methods, using two different iterative numerical commenting on techniques methods their applicability P8 Determine the numerical integral and the accuracy of engineering functions using two of the methods different methods