A new supercar has been launched by the Proton Company and the velocity can be expressed in the following function:
v(t) = 15t^3 + 30t^2 + 10t
where the unit velocity is measured in m/s and t in seconds. Determine the acceleration of the supercar at t = 3 by using:
(i) 3-point central difference
(ii) 5-point central difference
Use h = 0.0001.
(b) The rate of heat flow (conduction) between two points on a cylinder heated at one end is given by dQ = 1AdT/dx, where dQ is the heat flow, A is the cylinder's cross-sectional area, T is the temperature, t is the time, and x is the distance from the heated end.
Given that dT/dx = (100(L-x)(20-t))/(100-xt), where L is the length of the rod.
If the initial condition is Q(0) = 0 and the parameters are A = 10 cm, L = 20 cm, x = 2.5 cm, and d = 0.4 cal/cm/s, compute the heat flow for t = 0 to 25 s by using the Midpoint method. Use h = 5.