The acceleration of a particle moving along the x-axis is a = −0.2v², where a is the acceleration in ft/sec² and v is the velocity in ft/sec. At the origin, the velocity of the particle = is v 20 ft/sec. The velocity of the particle at position x = 10 ft is most nearly

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A particle moves along the x- axis. The function (t) gives the particle's position at any time t > 0: x(t) = t³ - 4t² + 3t - 2 What is the particle's velocity v(t) at t = 2?

Bungee Jump Simulation (Second order Ordinary Differential Equations) A team of engineering students is planning a bungee jumping trip. One of the preparation tasks is to write a MATLAB program to simulate high-altitude bungee jumping using a 150-meter bungee line. The purpose of the simulation is to estimate the peak acceleration, velocity, and drop distance of the jump to ensure that the arresting force of the bungee is not too great and the jump off point is high enough so that no one will hit the ground. The equation to use for the analysis is Newton's Second Law, F = ma where F is the sum of the gravitational, aerodynamic drag, and bungee forces acting on the jumper, m is the mass of the jumper (which is 70 kg), and a is the acceleration. Define the distance the jumper falls as the variable x (which is a function of time, x(t)). The jumper's velocity and acceleration are then represented as x' and x", respectively. The Newton's equation to solve for acceleration: x" = F/m Next,…