ng A particle starting from rest revolves with uniformly increasing speed in a clockwise circle in the zy plane The center of the circle is at the origin of an ay coordinate system. At t=0 the particle is at x=0.0,y=2.9mcdot Att=1.0s , it has made one- quarter of a revolution and is at x=y_(0),y=0.0 Part A Determine its speed at 1.0 s. Express your answer to two significant figures and include the appropriate units. ? m v=4.56 square Submit Previous Answers Request Answer & Incorrect; Try Again;One attempt remaining

To determine the speed of the particle at , we need to use the information given about its motion and the geometry of the circle.1. **Initial Position and Speed:** - At , the particle is at \( (x_0, y_0) = (0.0, 2.9 \, \text{m}) \). - The particle starts from rest, so its initial velocity .2Quarter Revolution:** - At , the particle has made one-quarter of a revolution. - One-quarter of a revolution corresponds to an angle of radians.3. **Circle Geometry:** - The center of the circle is at the origin. - The radius of the circle can be found using the initial position: .4. **Velocity after One-Quarter Revolution:** - After one-quarter of a revolution, the particle will be at \( (y_0, -x_0) = (2.9 \, \text{m}, -0.0) \). - The velocity component in the x-direction is . - The velocity component in the y-direction is .5. **Angular Velocity :** - The angular velocity can using the fact that the particle makes one-quarter of a revolution in 1 second: .6. **Components of Velocity:** - . - .7. **Speed Calculation:** - The speed is the magnitude of the velocity vector: \( v = \sqrt{v_x^2 + v_y^2} = \sqrt{(-2\pi)^2 + 0^2} = 2\pi \, \text{m/s} \).Therefore, the speed of the particle at is .Expressing this to two significant figures: So, the correct answer is: