Problem 02:The following data of the velocity of a body is given as a functicn of time.Time (s)Velocity (m/s) 0 24 37 75 1230 14 18 22 24Question 1:Determine the value of the velocity at t=19 seconds with first order polynomial interpolation using directpolynomial interpolation.Question 2:Determine the value of the velocity at t 19 seconds with first order polynomial interpolation using Newtonpolynomial interpolation.Question 3:Determine the value of the velocity at t= 19 seconds with first order polynomial inierpolation using Lagrangepolynomial interpolation.!3!

Introduction: Interpolation is a technique for constructing a basic function from a discrete data…

Answered: Problem 02: The following data of the…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(b) Towns A and B are 12 km apart. A cyclist leaves A and travels to B at an average speed of y km/h. From B, he returns immediately to A with an average speed reduced by 2 km/h. (i) Find, in terms of y, the time taken for the journey from A to B. (ii) Find, in terms of y, the time taken for the return journey. (iii) Given that the total time spent to travel from A toB and back to A is 5 hours, write an equation satisfied by y. (iv) Solve the equation written in part (iii). (v) Give a simple reason why one of the values of y obtained in part (iv) is not valid.
2. (b) Suppose instead that the true speed of the car as a function of time is described by v(t) = 30√t (still from t = 0 to t = 4). Sketch a graph of the car’s speed vs. time. (c) Since the speed is no longer constant, it is much harder to calculate the distance traveled. But we can still try. Suppose we wanted to just calculate how far the car went in the single minute from 1:00 and 1:01. Let’s pretend that the car’s speed is constant for this single minute. What might be a reasonable approximation for the car’s speed, in this scenario? Under this assumption, approximately how far did the car go during this minute? Represent the distance traveled during this one minute as an area in your diagram from part (b).
An object moves in such a way that its displacement s (in metres) as a function of time t (in seconds) is given by the equation of this object at Determine the acceleration s(t) = 2t - 9t +7t-1 seconds. t= 2 3 m/sec O 6 m/sec O 4 m/sec O 2 m/sec
(a) At any time t seconds, the distance x metres of a particle moving in a straight line from a fixed point is given by x = 4t² -3t+ In(1+3t) Determine expressions for the initial velocity and acceleration of the particle and their values after 3 seconds.
A4) The position of a hummingbird flying along a straight line in t seconds is given by S(t) = 2t - 20t meters. [ 1 mark ] (a) Determine the velocity of the bird at t = 3 sec. [0.25 mark] (b) Determine the acceleration of the bird at t = 3 sec. [0.25 mark] (c) Determine the acceleration of the bird when the velocity equals 0. [0.5 mark]
Part 2. Use the Newton-Raphson Method to solve the roots of the following functions: 3. f(x) = -6x² + 11x - 3.2 4. f(x) = 2x² + 4.5x-10

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