(a)At any time t seconds, the distance x metres of a particle movingin a straight line from a fixed point is given byx = 4t² -3t+ In(1+3t)Determine expressions for the initial velocity and acceleration ofthe particle and their values after 3 seconds.

The distance x meters is given we have to find the velocity and acceleration function and it's…

Answered: (a) At any time t seconds, the distance…

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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A researcher is nuning a simulation of an upward rocket to study the upward velocity of the rocket using various fuel consumption rates. The researcher has found that the upward velocity of the rocket can be represented by the following equation, mo v = u In gt Amo-qt. where v=upward velocity of the rocket (m/s), u= the velocity at which fuel is expelled relative to the rocket (m/s), m, = the initial mass of the rocket (kg), q = the fuel consumption rate (kg/s), g = the downward accelemation of gravity (m/s), and t = time taken by the rocket for the whole motion (s). If u = 1,500 m/s, m, = 125,000 kg, q = 2,300 kg/s and g= 9.81 m/s are the values used by the researcher in one of his simulations, estimate the time, t at which v = 680 m/s using False Position method. It is known that the time, t is somewhere between 15 s and 35 s. Perform THREE (3) iterations only and calculate the approximate percent relative error, Ea| for every iteration.

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(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.