The finished program is given below.
The complete program can be copied and pasted into an editor, and run in the usual way.
import java.io.*;
// User picks ending value for time, t.
// The program calculates and prints the distance the brick has fallen for each t.
//
class fallingBrick
{
  public static void main (String[] args ) throws IOException
  {
    final double G = 9.80665;   // constant of gravitational acceleration
    int    t, limit;            // time in seconds, and ending value of time
    double distance;            // the distance the brick has fallen
    BufferedReader userin = new BufferedReader (new InputStreamReader(System.in));
    String inputData;
    System.out.println( "Enter limit value:" );
    inputData = userin.readLine();
    limit     = Integer.parseInt( inputData );
    // Print a table heading
    System.out.println( "seconds\tDistance"  );
    System.out.println( "-------\t--------"  );
    t         = 0 ;
    while (  t <= limit )    
    {
      distance = (G * t * t)/2 ;
      System.out.println( t + "\t" + distance );
      t = t + 1 ;
    }
  }
}
You could also write distance = 0.5*G*t*t;.
What were the two traps in translating the formula?
If you translated it as 
(1/2)*G*t*t, 
you fell into the first trap.
(1/2)  asks for integer division of 1 by 2, resulting in zero.
If you translated the formulat as 
1/2*G*t*t, 
you fell into the second trap.
To the compiler,
this  looks  like the first wrong formula
(because "/" has equal precedence to "*").
A third problem is computing the square.
Do it as t
multiplied by t.