BITSAT 2011 Paper

When the mass increases by a factor of 4 theacceleration must decrease by a factor of fourif the same force is applied. The question asksabout position so we need to relateacceleration and time to position. We can do this by the equation : xf–xi = vxi t + ½ ax t2
We want the change in position to stay the same. The initial velocity is zero so in order for the change in position to remain constant the term (1/2) at2 must remain the same. If the acceleration is reduced by a factor of 4 you can see that the time must be increased by a factor of 2 in order for the term to remain the same.