Chapter 12, Problem 6P

3. The motion of the particle along a straight line is governed by the relation a = t³ – 2t2 + 7 where a is the acceleration in m/s? andt is the time in seconds. At time t velocity of the particle is v m/s and the displacement is d m. Calculate the displacement, velocity and acceleration at time t = 2 seconds. * A second, the 0.5 А second V = ..m/s d 25 m

A particle moves along a path according to the equations      x = 9 - t4/9  and  y = t2/3 where x and y are in meters and t is in seconds. Determine the magnitude of the velocity (in m/s) of the particle in 1.97 seconds.

The particle travels along the path defined by the parabola y = 0.5x², where x and y are in ft. When t = 0, x = 0, y = 0. (Figure 1) Figure y -y = 0.5x² Part A If the component of velocity along the axis is v₂ = (2t) ft/s, where t is in seconds, determine the particle's distance from the origin O when t = 3 s. Express your answer using three significant figures and include the appropriate units. ► View Available Hint(s) d = 10.06 O Part B Submit Previous Answers X Incorrect; Try Again μA a = | ft Determine the magnitude of the particle's acceleration when t = 3 s. Express your answer using three significant figures and include the appropriate units. ► View Available Hint(s) μA Value P BR Units ? P Pearson ? Review

Dynamics

At time t = 0, the position vector of a particle moving in the x-y plane is r = 5.28i m. By time t = 0.022 s, its position vector has become (5.39i+ 0.48j) m. Determine the magnitude Vay of its average velocity during this interval and the angle 8 made by the average velocity with the positive x-axis. Answers: Vav 0 = = 20 i m/s

Q3/ A particle moving along a straight line is subjected to a deceleration a = (- V) m/s², where is V in m/s. If it has a velocity V-5m/s and a position S=10 m when t = 0, determine its velocity and position when t = 4 s.

Dynamics of Rigid Bodies - Mechanical Engineering The velocity of a particle moving in the x-y plane is given by (6.91i + 7.17j) m/s at time t = 5.61 s. Its average acceleration during the next 0.017 s is (2.7i + 4.3j) m/s^2. Determine the velocity v of the particle at t = 5.627 s and the angle O between the average-acceleration vector and the velocity vector at t = 5.627 s. Subject: Mechanical Engineering

The velocity of a particle moving in the x-y plane is given by (3.46i +7.64j) m/s at time t = 4.88 s. Its average acceleration during the next 0.030 s is (2.1i + 2.0j) m/s². Determine the velocity v of the particle at t = 4.910 s and the angle between the average- acceleration vector and the velocity vector at t = 4.910 s. Answers: V = (3.523 7.7 j) m/s 0: = i 22.032 O

The horizontal motion of the plunger and shaft is arrested by the resistance of the attached disk which moves through the oil bath. The velocity of the plunger is v0 = 3.8 m/s in the position A where x = 0 and t = 0, and the deceleration is proportional to v so that a = -kv where k = 0.61 s-1. Find (a) the velocity when t = 5.5 s, (b) the position x when t = 5.5 s, (c) the velocity when x = 3.5 m.