Question

Find magnitude of velocity and acceleration at t=1

Part A Learning Goal To be able to calculate position, velocity, and acceleration of an object in curvilinear motion using a rectangular coordinate system. A car drives on a curved road that goes down a hill. The car's position is defined by the position vector An object's motion can be described along a path represented by a fixed x, y, z coordinate system. In such a system, the position vector, r, is described A 15.0ft/s. The image below shows the system projected onto the x-y plane. What are the car's velocity and acceleration vectors at this position? as Draw your vectors starting at the black dot. The orientation of your vectors will be graded. The exact length of your vectors will not be graded and the trigonometric function arguments are in radians The object's velocity, v, can be found by taking the first time derivative of the position vector, r: View Available Hint(s) The object's acceleration, a, can be found by taking the time derivative of the velocity, v: No elements selected s selected Learning Goal: To be able to calculate position, velocity, and acceleration of an object in curvilinear motion using a rectangular coordinate system. An object's motion can be described along a path represented by a fixed x, y, z coordinate system. In such a system, the position vector, r, is described as The object's velocity, v, can be found by taking the first time derivative of the position vector, r: The object's acceleration, a, can be found by taking the time derivative of the velocity, v: 30 ft dty Part B Learning Goal What is the magnitude, v, of the cars velocity, v, at t 1.00 s? To be able to calculate position, velocity, and acceleration of an object in curvilinear motion using a rectangular coordinate system Express your answer numerically in feet per second to three significant figures. View Available Hint(s) An object's motion can be described along a path represented by a fixed Х.Х z coordinate system. In such a system, the position vector, r, is described as The object's velocity, v, can be found by taking the first time derivative of the position vector, ir: Submit Previous Answers The object's acceleration, a, can be found by taking the time derivative of the velocity, v: X Incorrect; Try Again; 5 attempts remaining

Answer 1

$\vec{r}=-30\cos\bigg(\frac{\pi}{10}t\bigg)\hat{i}+30\sin\bigg(\frac{\pi}{10}t\bigg)\hat{j}-15t\,\hat{k}$

dr cost 15k . COS 10 10 V) 10 10 dt

= 3π sin に1 j-15 k-2.912i + 8.963j-15k

últ=1_ V2.9122 + 8.9632 + 15.02 = 17.7 ft/s