Select the correct answer. A bubble originating at the bottom of a lake rises to the surface within 10.0 seconds with an acceleration 10.0meters/second^2 What is the depth of eration of the lake? A. 100 meters B. 200 meters C. 300 meters D. 400 meters E. 500 meters

To solve this problem, we can use the equation of motion for uniformly accelerated motion:<br /><br />\[ s = ut + \frac{1}{2}at^2 \]<br /><br />where:<br />- \( s \) is the displacement (the depth of the lake),<br />- \( u \) is the initial velocity (which is 0 m/s since the bubble starts from rest),<br />- \( a \) is the acceleration (10.0 m/s\(^2\)),<br />- \( t \) is the time (10.0 seconds).<br /><br />Plugging in the values, we get:<br /><br />\[ s = 0 \cdot 10.0 + \frac{1}{2} \cdot 10.0 \cdot (10.0)^2 \]<br />\[ s = \frac{1}{2} \cdot 10.0 \cdot 100 \]<br />\[ s = 500 \text{ meters} \]<br /><br />Therefore, the correct answer is:<br /><br />E. 500 meters