4. A stunt plane flying at the Reno Air Races is moving through the sky. The rectangular coordinates describing its motion are: x = -0.74t³ + 2.5t² + 10.25t y = -6.23t² + 16.45t + 8.94 where x and y are given in ft and t is given in seconds. a. Calculate the velocity vector, v, and acceleration, a, of the plane after 10 seconds (velocity is in ft/s and acceleration is in ft/s²). You may want to look back at your Topic 2 notes to recall how position, velocity, and acceleration are related. Your final answer should be given in vector form. b. Calculate the magnitude of the velocity (in mph) and the acceleration (in ft/s²) at t = 10 sec. [Ans. to Check: v= 132.46 mph; a = 41.32 ft/s²]

Provide complete solutions with the derivation of formulas integrals and derivatives

This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. From measurements of a photograph, it has been found that as the stream of water shown left the nozzle at A, it had a radius of curvature of 17 m.   Determine the initial velocity vA of the stream. (You must provide an answer before moving on to the next part.)   The initial velocity is m/s ⦨⦨ 36.9°.?   Note: please show step by step solution. Hence, double check the solution. For correction purposes!. I require  handwritten working out please!. Kindly, please meticulously, check the image for conceptual understanding and for extra information purposes!. Also on occasions, I receive wrong answers!!. Please go through the question and working out step by step when you finish them. Appreciate your time!.

Q No 1:  The position of a particle moving along the x-axis is given by x=A+B t3,              where A=9.75 cm and B=1.50cm/s3.consider the time interval t=2 to t=3s and             calculate (a).the average velocity; (b).the instantaneous velocity at t=2s;(c). the             instantaneous velocity at t=3s;(d). the instantaneous velocity at t=2.5s;(e). the             instantaneous velocity when the particle is midway between its positions at t=2s             and t=3s.

Question 2: The applied force P causes block B to accelerate at ab = 5 Xb 0.25x ft/s², where x, is the position of block B measured from fixed point D. Initially, x, = 0.5 ft and the blocks are at rest. When x = 3 ft, find: a) The velocity and acceleration of B relative to A b) The absolute velocity of point C on the cable CA D- For each answer, report whether the direction is to the right or the left. -

1 Velocities are measured at different locations using a data logger and the field is given by the technician in the following vector form. Given that. du du ax = +u-+v. +w du du ôt əx ду əz V = 3tî +xzj+t Find the magnitude of velocity and acceleration at point (1,1,1) at time t = 1 second. Write the acceleration vector. If the fluid is incompressible, show that the flow field satisfies the conservation of mass. zj+ty²k m/s Əv dv dv Əv +u- +v +w- at Əx ду əz dw dw dw dw + w a ₂ = +u Ət Əx dy əz +v

Consider the motion of a soccer ball that is kicked from the point (Xo-Yo) = (0,0) with an initial velocity of (uovo) = (40,8) m/s. Assume the x-axis is horizontal, the positive y-axis is vertical (opposite g), the ground is horizontal, and only the gravitational force acts on the object. a. Find the velocity and position vectors for t≥ 0. b. Graph the trajectory. c. Determine the time of flight and range of the soccer ball. d. Determine the maximum height of the soccer ball.

Applying principles of dynamics (written detailed solution please tysm!) The displacement of a particle which moves along the x axis is given by x = (-4 + 3t2)e-0.25t, consider x to be in feet and t in seconds. Plot the displacement, velocity and acceleration for the first 20 seconds of motion and determine, both graphically and by your established equation for acceleration, the time at which acceleration is 0. (If you find it more comfortable to practice, you may choose to graph using excel or any graphing software, solutions however must be done manually).

Figure Q1(b) shows a train travelling along a circular curve of a radius r = 300 m. Atthe instant shown, its angular rate of rotation is 0.03 rad/s which is decreasing at0.0015 rad/s2. Calculate the magnitude of train’s velocity at this instant shown andalso calculate the magnitude and direction of the train’s acceleration at this instant.

Find the position vector for the maximum position of the particle expressed in format R= Xi+ Yj