PROBLEM 2 (10 POINTS) A particle moves with constant velocity u along the curve r =...
Problem #1 (35 Points) Given The velocity of a particle as it moves along a straight line is given by v (-12+36t-6t2) ft/s, where t is in seconds. At the initial condition ( 0), so 2 ft. Find a) The acceleration of the particle as a function of time. b) The acceleration of the particle when -6 seconds. c) The position of the particle as a function of time. d) The position of the particle when -6 seconds. e) The...
L. PA AC 0 Particle A moves along a circular path (of radius R) with constant speed 4. Particle B moves along a straight-line path with constant speed vs. Circle the appropriate answer below relative to the position shown. • The velocity of Particle A with respect to Particle B is: vh UB) (UB-u) (U+08) • The acceleration of Particle A with respect to Particle B is: (uB-) R R
PROBLEM 2 (10 POINTS) A particle of mass m moving along a straight line is acted on by a retarding force (one directed against the motion) F = beau, where b and a are constants and u is the velocity. At に0, it is moving with velocity 10. Find the velocity at later times always
Problem 4*: (Motion along a spiral) A particle of mass m moves in a gravitational field along the spiral z = k0, r = constant, where k is a constant, and z is the vertical direction. Find the Hamiltonian H(z, p) for the particle motion. Find and solve Hamilton's equations of motion. Show in the limit r = 0, 2 = -g.
7. A point P moves along the spiral rae20 with constant speed u. Show that the components of its velocity along and perpendicular to the radius vector are constant. Find in terms of u and r the magnitude of the resultant acceleration of P. Find the angle between this acceleration and the velocity of P 7. A point P moves along the spiral rae20 with constant speed u. Show that the components of its velocity along and perpendicular to the...
please answer all questions For 1 2 0, a particle moves along the r-axis. The velocity of the particle at time t is given by r(t)-1 + 2sin(2) Theparticle is atposition x = 2 attimet=4. (a) At time t-4, is the particle speeding up or slowing down? (b) Find all times t in the interval o<t<3 when the particle changes direction. Justify your answer. (c) Find the position of the particle at time t 0. (d) Find the total distance...
EX #1: For t > 0, a particle moves along a curve so that its position at time t is (x(t), y(t)), where x(t) = 4t and = 1 - 2t. Find the time t at which the speed of the particle is 5.
3. The particle moves along a planar curve y = et, where r and y are measured in meters. It has a constant speed v = 12 m/s. Then the tangential and normal components of acceleration are at = m/s2 and an = m/s2 at y= 1 m. (Express the answer to two significant p=(1+roji figures. Hint: ) = (TT51FTS) 13: 23:
A particle moves along a straight a) The average velocity on the line with equation of motion interval [3,4] s= f(t) = t? - 60 + 10, b) The instantaneous velocity. Where S is measured in meters and t in seconds. find the C) The instantaneous velocity when following: t = 4 seconds. The growth of a bacterial population is represented by the function f(t) = 1 + 5t - 2t2 Where t is the time measured in hours find...
For t ≥ 0, a particle moves along the x-axis. The velocity of the particle at time t is given by v(t)=1+2sin(t^2/2). The particle is at x=2 at time t=4. a)Find position of particle at t=0 b)Find the total distance the particle travels from time t=0 to time t=3