(a) Between the backward, forward and central difference formulas, which method give more accuracy in approximation for numerical differentiation. Explain why.
(4 marks)
(b) The following data were collected for the distance travelled versus time for a rocket as shown in Table 4:
able[[Table 3],[t,s,0,25,50,75,100,125],[y,km,0,32,58,78,92,100]]
Use numerical differentiation to estimate the rocket's velocity and acceleration at each time recorded. Using central differences everywhere possible, and a forward or backward difference where a central difference is not possible, to calculate the velocity and the acceleration.
(a Between the backward,forward and central difference formulas,which method give
more accuracy in approximation for numerical differentiation.Explain why
(4 marks)
(b) The following data were collected for the distance travelled versus time for a rocket as
shown in Table 4:
Table 3
t, s
0
25 32
50 58
75
100 92
125
y, km
0
78
100
Use numerical differentiation to estimate the rocket's velocity and acceleration at each
time recorded. Using central differences everywhere possible, and a forward or
backward difference where a central difference is not possible,to calculate the velocity
and the acceleration