Question

A force acts an a 3g particle in such a way that the position of the particle as a function of time is given by x=3t-4t^2+t^3, where x is in metre and t is in second. The work done during the first 4s is

Answer 1

weight is 3gm = 0.003 Kg 
after double integration of x we got acceleration = 6t -8 and in 4 sec 
a = 16 m/sec^2
so F = ma = 0.003 x 16 = 0.048 N
and distance in 4 second x = 64 -64+12 = 12 m 
so
workdone = F.S = 0.048 x 12 = 0.576 N-m

regards