A body of mass 10 kg is kept on ground.A vertically upwards force F=20t N,where t is the time in seconds,starts acting on it at t=0.The height of the block from ground at t=10 sec is n*25/3,where n is a constant.Find n.

You can use integral of Sum of F dt = integral of m dv. The only trick here is to note that the block doesn't start to move until F exceeds the force of gravity, so you only need to evaluate the integral from t= 5 seconds to t=10 seconds.