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). Solve the following: (i) Approximate SIX (6) values of the car's velocity at t = 7.5min using appropriate difference formula and a consistent step size. Answers must be in 3-decimal points.

Advanced Engineering Mathematics
10th Edition
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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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). Solve the following:
Q2
(a)
Approximate SIX (6) values of the car's velocity att = 7.5min
using appropriate difference formula and a consistent step size.
Answers must be in 3-decimal points.
(i)
(ii)
Which of the formula that you used in Q2(a)(i) potentially could
provide the best approximation? Give a justification for your
answer.
(iii)
Find the approximate acceleration of the car (in 3-decimal
points) at distance 12km by considering as much data as
possible.
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). Solve the following: Q2 (a) Approximate SIX (6) values of the car's velocity att = 7.5min using appropriate difference formula and a consistent step size. Answers must be in 3-decimal points. (i) (ii) Which of the formula that you used in Q2(a)(i) potentially could provide the best approximation? Give a justification for your answer. (iii) Find the approximate acceleration of the car (in 3-decimal points) at distance 12km by considering as much data as possible.
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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