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 xy coordinate system. Att=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 e the appropriate units. ? m v=3.35 square Submit Previous Answers Request Answer Incorrect; Try Ağain;4 attempts remaining

To determine the speed of the particle at 1.0 s, we need to use the relationship between velocity and angular displacement in circular motion.<br /><br />Given:<br />- The particle starts from rest, so its initial velocity \( v_0 = 0 \).<br />- At \( t = 0 \), the particle is at \( (x_0, y_0) = (0, 2.9 \, \text{m}) \).<br />- At \( t = 1.0 \, \text{s} \), the particle is at \( (x, y) = (y_0, 0) \).<br /><br />Since the particle makes one-quarter of a revolution in 1.0 s, the angular displacement \( \theta \) is \( 90^\circ \) or \( \frac{\pi}{2} \) radians.<br /><br />The relationship between linear velocity \( v \), angular velocity \( \omega \), and radius \( r \) is:<br />\[ v = \omega r \]<br /><br />The angular velocity \( \omega \) can be found using the formula:<br />\[ \omega = \frac{\Delta \theta}{\Delta t} \]<br /><br />Here, \( \Delta \theta = \frac{\pi}{2} \) radians and \( \Delta t = 1.0 \, \text{s} \):<br />\[ \omega = \frac{\frac{\pi}{2}}{1.0 \, \text{s}} = \frac{\pi}{2} \, \text{rad/s} \]<br /><br />The radius \( r \) of the circle is the distance from the origin to the initial position of the particle:<br />\[ r = \sqrt{x_0^2 + y_0^2} = \sqrt{0^2 + 2.9^2} = 2.9 \, \text{m} \]<br /><br />Now, we can find the speed \( v \):<br />\[ v = \omega r = \left(\frac{\pi}{2} \, \text{rad/s}\right) \times (2.9 \, \text{m}) \]<br />\[ v = \frac{\pi \times 2.9}{2} \, \text{m/s} \]<br />\[ v \approx \frac{9.0816}{2} \, \text{m/s} \]<br />\[ v \approx 4.54 \, \text{m/s} \]<br /><br />Therefore, the speed of the particle at 1.0 s is approximately \( 4.5 \, \text{m/s} \).