<p>For a train engine moving with speed of 20&nbsp;<span class="equation">\(ms^{-1}\)</span>, the driver must apply brakes&nbsp;at a distance of 500 m before the station for the train to come to rest at the station. If the brakes were applied at half of this distance, the train engine would cross the station with speed&nbsp;<span class="equation">\(\sqrt{x} \)</span>&nbsp;<span class="equation">\(ms^{-1}\)</span>​. The value of x is____.</p>

<p>​​​​​​(Assuming same retardation is produced by brakes)</p>