The three components are as follows: u = 2xt– 3xyz + 6z v = x– yz + 4xyt w = 3x– 5yzt + yz Find the velocity and acceleration of a fluid particle at (1, 0, 1) at time, t = 0.

b. The velocity vector in a fluid flow is given as V = 4x³i – 10x²yj + 2tk . Find (i) The velocity of a fluid particle at (2, 1, 3) at time t=1. (ii) The acceleration of a fluid particle at (2,1,3) at time t =1.

The velocity vector in a fluid flow is given by V = 2xy3i – 5x2yj + 4xyztk. Find the velocity and acceleration of a fluid particle at (1, 2, 1) at time, t = 0.

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Dynamics

Tp = Fq +°P/Q• (1) Here ip/Q is the "position of point P relative to point Q." Similarly the velocities of the two points are related by õp = bq + Up/Q- (2) The quantity õp/Q is the velocity of point P relative to point Q. I want you to use these ideas to solve the following problems. 1. The figure below shows a view from above of a large boat in the middle of the ocean. So that the crew on the ship can get exercise on long journeys, there is a circular walking/running track on the back deck. CA B- -D Suppose that the radius of the track is R = 6 m, and a person is running on the track at a constant speed of v = 3m/s as measured with a stopwatch by a crew-mate on board the ship. Suppose the runner is running counter-clockwise around the track when viewed from above. Write the velocity vector of the runner in terms of basis (ê1, ê2) as perceived by a crew-mate on the ship. (a) What is the velocity vector when the runner is at point A? (b) What is the velocity vector when the runner is…

Given the Eulerian velocity vector field: V = 3ti + xzj + ty²k Find the total acceleration of a particle av av av W дх' ду' ду Hint: u V

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

Example (3): A body moves on a straight line according to the equation: S = 4 t + 2 t2- 2 t + 5, where (s) is displacement, (t) is the time interva , Find out displacement, velocity , and acceleration when t= 3 sec . Solution: 2 12 - 2 t+ 5