Give an algorithm to calculate an approximation to the

Question

Using a GPS we have m all speed v of an object moving . Measurement might have been made by N + 1 times (t_i)_i=0^N( from i = 0 to N) such that the result is a sequence of numbers pairs ( t_i, v_i)_i=0^N(from i = 0 to N) which we specify the speed at time t_i.

a. Give an algorithm to calculate an approximation to the object akselle- ration a (t) = v ' (t) from the calculated values (t_i, v_i) of speed.

b. Give an algorithm to calculate an approximation to the object's distance s ( t) from the starting point from the calculated value when v (t) = s' (t) and s (t₀) = 0.