Calculating Cube Deceleration on a Moving Board

[caseys]

A 0.5m cube is sitting on top, and at the end, of a 1m wide by 3m long board. Both the cube and board are traveling at a constant velocity of 10 m/s. The board begins to decelerate at -8.5 m/s squared. The cube decelerates across the top of the board at -3 m/s squared. How much time will it take for the cube to move 1.5 meters across the top of the board.

I can figure the problem out if the board was not moving but am stuck in trying to figure out how the board decelerating faster will affect the deceleration of the cube.

 

[HallsofIvy]

If the board is decelerating at -8.5 m/s^{2 and and the box is decelerating at -3 m/s2, then, relative to the board[\b], the box is accelerating at -3- (-8.5)= 5.5 m/s2. Now just do it as if the board were not moving.}

 

[caseys]

Got it! Thanks...
Casey