Estimate the velocity at t = 6 sec using the 2-point reverse estimate for the fi

Question

Estimate the velocity at t = 6 sec using the 2-point reverse estimate for the first derivative. Be sure to show your work and include units!

2-point Estimate of Velocity at t = 6 sec: _________

Estimate the velocity at t = 6 sec using the 3-point estimate for the first derivative. Again, show work and include units!

3-point Estimate of Velocity at t = 6 sec: ______

Problem 2: Using the same position data from Problem 1, estimate the acceleration at t = 9 sec using the numerical estimate for 2nd derivative. Again, show work and include units! Estimate of Acceleration at t = 9 sec: ______

Explanation / Answer

deltaT=.5
1)2-point Estimate of Velocity at t = 6
v=(x(6)-x(6-deltaT))/deltaT
v=(x(6)-x(5.5))/.5
v=(10-12).5=-4 cm/s

2)3-point Estimate of Velocity at t = 6 sec
v=((x(6+deltaT)-x(6))+(x(6)-x(6-deltaT)))/(2*deltaT)
v=((x(6.5)-x(6))+(x(6)-x(5.5)))/1
v=(7-10)+(10-12)=-5 cm/s

Problem 2)using center difference for second derivative
a=(x(9+deltaT)-2*x(9)+x(9-deltaT))/(deltaT*deltaT)
a=(x(9.5)-2*x(9)+x(8.5))/.25
a=(11-2*4+1)/.25
a=16 cm^2/s

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