Answer to Question #74145 in Quantitative Methods for AJIT SINGH

Question

the position of f(x) of a particle moving in a line at various times xk is given in the following table. estimate the velocity and acceleration of the particle at x =1.2. f(1.0)=2.72, f(1.2)=3.32, f(1.4)=4.06, f(1.6)=4.96, f(1.8)=6.05, f(2. 0)=7.39, f(2.2)=9.02.

Answer 1

velocity at x =1.2 :

v(1.2)=f^' (1.2)=(f(1.2)-f(1.0))/(1.2-1.0)=(3.32-2.72)/0.2=3

acceleration at x =1.2 :

a(1.2)=f^'' (1.2)=(f(1.4)-2f(1.2)+f(1.0))/〖0.2〗^2 =(4.06-2∙3.32+2.72)/0.04=3.5