At time
t = 1,
a particle is located at position
(x, y) = (4, 5).
If it moves in the velocity field
F(x, y) =
xy − 3, y2 − 8
find its approximate location at time
t = 1.03.
At time t = 1, a particle is located at position (x, y) = (4, 5)....
At time t = 1, a particle is located at position (x,y) = (3,1). If it moves in the velocity field F(x,y) = <xy - 3, y2 - 9> find its approximate location at time t = 1.02. (x,y) = (_____)
At time t = 1, a particle is located at position (x,y) = (2, 3). If it moves in the velocity field F(x, y) = (xy - 2, y2 - 12) find its approximate location at time t = 1.05. (x, y) = ( 2.15,2.95 x
At time t = 1, a particle is located at position (x, y) = (3, 2). If it moves in the velocity field F(x, y) = xy − 1, y2 − 9 find its approximate location at time t = 1.04.
9. A particle moves along the x-axis so that its velocity v at time t, for0 sts 5, is given by v(t) In(t2-3t +3). The particle is at position x 8 at time t 0. a) Find the acceleration of the particle at time t 4. b) Find all times t in the open interval 0<t <5 at which the particle changes direction. During which time intervals, for 0st s 5, does the particle travel to the left? c) Find...
Mechanics. Need help with c) and d)
1. A particle of mass m moves in three dimensions, and has position r(t)-(x(t), y(t), z(t)) at time t. The particle has potential energy V(x, y, 2) so that its Lagrangian is given by where i d/dt, dy/dt, dz/dt (a) Writing q(q2.93)-(r, y, z) and denoting by p (p,P2, ps) their associated canonical momenta, show that the Hamiltonian is given by (show it from first principles rather than using the energy) H(q,p)H(g1, 92,9q3,...
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
3.) The position of a particle is given by x(t) = 3t3 – 2t2 – 5t + 10, where t is in seconds and x is in meters. Find the initial position of the particle. Find the position of the particle after 5 seconds. Find the average velocity from 0 sec to t = 5sec Find the instantaneous velocity as a function of time Find the instantaneous velocity at t = 2 seconds. Find the instantaneous velocity at t=4 seconds...
Average and Instantaneous Velocity A particle moves along the x axis. Its position varies with time acording to the expression x =-4t + 2t2, where x is in meters and t is in seconds. The position-time graph for this motion is shown in the figure. Notice that the particle moves in the negative x direction for the first second of motion, is momentarily at rest at the moment t = 1 s, and moves in the positive x direction at times...
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.
4. A particle starts from an initial position with coordinates To = 8 + 5ſm, at time t= 0, with a velocity of V. = 3i-8 m/s. The particle moves in the r-y plane with a constant acceleration, à = -21 - m/s. (a) At the instant the y-coordinate of the particle's position is -10 m, find the x- coordinate of its position. (b) Calculate the x- and y-components of the particle's position when the particle reaches its turning point...