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

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,…

The x-coordinate of a particle in curvilinear motion is given by x = 3.8t3 - 2.6t where x is in feet and t is in seconds. The y-component of acceleration in feet per second squared is given by ay = 3.9t. If the particle has y-components y = 0 and vy = 5.2 ft/sec whent = 0, find %3D %3D the magnitudes of the velocity v and acceleration a when t = 5.3 sec. Sketch the path for the first 5.3 seconds of motion, and show the velocity and acceleration vectors for t = 5.3 sec. Answers: V = i ft/sec a = ft/sec2

Example 2:A particle moving along a straight line is subjected to a deceleration a = (-2v') m/s², where v is in m/s. If it has a velocity v = 8 m/s and a position s = 10 m when 0, determine its velocity and position when t = 4 s. t = %3D

2/61 The velocity of a particle moving in the x-y plane is given by 6.12i + 3.24j m/s at time t age acceleration during the next 0.02 s is 4i + 6j m/s². Determine the velocity v of the particle at t = 3.67 s and the angle 0 between the average-acceleration vector and the velocity vector at t = 3.67 s. 3.65 s. Its aver-

Each of four particles move along the x-axis. Their positions (in meters) as functions of time (in seconds) are given as follows: Particle 1: (t) = 3.5 - 2.7³ Particle 2: (t) = 3.5+ 2.7+³ Particle 3: x (t) = 3.5 - 2.7² Particle 4: x (t) = 3.5-3.4t - 2.7t² Which of these particles have constant acceleration? O Only 1 and 2 Only 3 and 4 None of them Only 2 and 3 O All of them

The position of a particle moving along the x-axis is described by    x= t^3-108t in   where t is the time in seconds. For the time interval t=0 to t=10s. (a) plot the position, velocity, and acceleration as functions of time; (b) find the displacement of the particle: and (c) determine the distance traveled by the particle.

Starting at x = -18 m at time t = 0 s, an object takes 18 s to travel 46 m in the +x direction at a constant velocity. On a sheet of paper, make a position vs. time graph of the object's motion. What is its velocity?

Subject: DYnamics