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Q2 (a) Table Q2 (a) gives the values of distance travelled by a car at various times from a traffic light. Given that velocity, v = x' (t) and acceleration, a = v' (t). (i) (ii) Determine approximate SIX (6) values of the car's velocity at t = 7.5 min using appropriate difference formula and a consistent step size. Answers must be in 3 decimal places. Based on the Q2 (a)(i), suggest the method that could potentially provide the best approximation. Give a justification for your answer.

Q2 (a) Table Q2 (a) gives the values of distance travelled by a car at various times from a traffic light. Given that velocity, v = x' (t) and acceleration, a = v' (t). (i) (ii) Determine approximate SIX (6) values of the car's velocity at t = 7.5 min using appropriate difference formula and a consistent step size. Answers must be in 3 decimal places. Based on the Q2 (a)(i), suggest the method that could potentially provide the best approximation. Give a justification for your answer.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Table Q2 (a) gives the values of distance travelled by a car at various times from a traffic light. Given that velocity, v = x'(t) and acceleration, a = v'(t). Q2 (a) Determine approximate SIX (6) values of the car's velocity at t= 7.5 min using appropriate difference formula and a consistent step size. Answers must be in 3 decimal places. (i) Based on the Q2 (a)(i), suggest the method that could potentially provide the best approximation. Give a justification for your answer. (ii) Estimate the approximate acceleration of the car (in 3 decimal places) possible. (iii) a distance of 12 km by considering as much data as
Transcribed Image Text:Table Q2 (a) gives the values of distance travelled by a car at various times from a traffic light. Given that velocity, v = x'(t) and acceleration, a = v'(t). Q2 (a) Determine approximate SIX (6) values of the car's velocity at t= 7.5 min using appropriate difference formula and a consistent step size. Answers must be in 3 decimal places. (i) Based on the Q2 (a)(i), suggest the method that could potentially provide the best approximation. Give a justification for your answer. (ii) Estimate the approximate acceleration of the car (in 3 decimal places) possible. (iii) a distance of 12 km by considering as much data as
Table Q2(a): Distance as a function of time. Time,t (min) Distance,x (km) 3.0 4.600 4.0 6.271 4.5 7.055 5.0 8.030 5.5 8.518 6.5 10.996 7.0 12.000 7.5 13.222 8.5 15.007 9.0 16.285 9.5 17.200 10.0 18.096 11.00 19.904
Transcribed Image Text:Table Q2(a): Distance as a function of time. Time,t (min) Distance,x (km) 3.0 4.600 4.0 6.271 4.5 7.055 5.0 8.030 5.5 8.518 6.5 10.996 7.0 12.000 7.5 13.222 8.5 15.007 9.0 16.285 9.5 17.200 10.0 18.096 11.00 19.904
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