What must be the initial velocity of a rocket that accelerates ; for 10.0 seconds at 5.00 m/s^2 and covers 4000. m? 150.m/s 375m/s 300.m/s -100.m/s

To find the initial velocity of the rocket, we can use the kinematic equation:<br /><br />\[ s = ut + \frac{1}{2}at^2 \]<br /><br />where:<br />- \( s \) is the displacement (4000 m),<br />- \( u \) is the initial velocity,<br />- \( a \) is the acceleration (5.00 m/s²),<br />- \( t \) is the time (10.0 seconds).<br /><br />Given:<br />\[ s = 4000 \, \text{m} \]<br />\[ a = 5.00 \, \text{m/s}^2 \]<br />\[ t = 10.0 \, \text{s} \]<br /><br />We need to solve for \( u \):<br /><br />\[ 4000 = u \cdot 10.0 + \frac{1}{2} \cdot 5.00 \cdot (10.0)^2 \]<br /><br />\[ 4000 = 10u + \frac{1}{2} \cdot 5.00 \cdot 100 \]<br /><br />\[ 4000 = 10u + 250 \]<br /><br />\[ 4000 - 250 = 10u \]<br /><br />\[ 3750 = 10u \]<br /><br />\[ u = \frac{3750}{10} \]<br /><br />\[ u = 375 \, \text{m/s} \]<br /><br />So, the initial velocity of the rocket must be \( 375 \, \text{m/s} \).<br /><br />The correct answer is \( 375 \, \text{m/s} \).