Problem 1 A particle moves along the curve x2 = 12y, where x and y are measured in millimeters. The x coordinate varies with time according to x = 4t2 – 2 mm, where t is in seconds. When t =2s, 1.1 Find the magnitude of the velocity vector 1.2 Find the magnitude of the acceleration vector

1. A box slides down a ramp with position vector given by r= 0.5t i + 3f² j + 8t k (m), where t is in s. At t = 3 s, what is the box's velocity and acceleration? What is the box's speed?

The motorcycle is traveling at 8 m/s when it is at A. The speed is then increased at v = 0.2 m/s² . (Figure 1) Figure y = 0.5x² 1 of 1 x Part A Determine the speed of the motorcycle at the instant t = 7 s. Express your answer to three significant figures and include the appropriate units. V = Submit Part B a = 0 Value μA Submit Request Answer Determine the acceleration of the motorcycle at the instant t = 7 s. Express your answer to three significant figures and include the appropriate units. μÀ Value Units Request Answer 2 Units ? ?

SOLVE CAREFULLY!! Please Write Clearly and Box the final Answer for Part A, with THE CORRECT UNITS ( should be rad/sec^2) Thank you. Express your answer to three significant figures and include appropriate units. DRAW the kinematic diagram and label it

Vp = A camera tracks the position of a particle moving along the given path with b = 10 m. At the moment shown, the camera angle is 0 = 40°, and the camera is rotating at 0 = 0.3 rad/s, which is accelerating at a rate 0 = 0.2 rad/s². What are the radial and transverse components of velocity and acceleration at this instant? vo = Ar = ao 0 || r = b sin(20) m/s m/s m/s² m/s²

Provide complete solutions with the derivation of formulas integrals and derivatives

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]

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