A block of mass 3kg rests on a smooth horizontal table. Starting at t=0, a horizontal force given by F=6tN (where t is in seconds) acts on the block for 5s. The initial velocity of the block is 2m s−1 toward the right.
a. (i) Draw the free-body diagram of the block showing all external forces acting on it while the horizontal force is applied.
b. (ii) Calculate the instantaneous acceleration of the block as a function of time t during the interval 0≤t≤5s.
c. (iii) Obtain an expression for the velocity of the block as a function of time in the same interval, and find its value at t=5s.
d. (iv) Determine the total displacement of the block in the first 5s.