hi friends will solve problem on dilemmas principle this is what is given in problem the 350 Newton box rest on horizontal for which coefficient of kinetic friction is ĩk equal to 0.32 if the box is subjected to a 400 Newton towing force as shown find the velocity of box in 4 seconds starting from rest that means in this case what is given this block is having some weight equal to 350 Newton towing force means what pull type of forces acting inclination is 30 degree the boss’s box is subjected to a force of 400 Newton find a velocity of box in 4 seconds starting from rest that means initial velocity is zero after 4 second you find out velocity will find out acceleration of block box once we’ll get acceleration of this box using equations of kinematics we’ll find out its velocity let me first step is what initial velocity is what 0 you have to find out what final velocity at T equal to 4 seconds therefore using this equation V equal to u plus a into T that means velocity equal to u 0 acceleration into 4 that means velocity equal to 4a that means what you have to do now simply find out acceleration of block applying the reverse principle to find out the acceleration of this block I draw a free body diagram in every day weight 350 Newton given 400 Newton to inputs ĩ is what 0.3 to draw a British this one next to pick is a beauty of box now this one box is initially at rest say this one is your reference like now which forces acts here we talk this box where top box is given how much is a weight above 350 Newton what external force is acting here is nothing but 400 in Newton inclined at an angle of 30 degrees with horizontal the normal reaction acts on the block normal reaction and normal to the contact surface that means in upward direction this is what RN now due to this 400 Newton definitely body or box will accelerate in the rightward direction frictional force will get in leftward direction ĩ is given as a point 3 2 3 2 RN this is nothing but free water important force what is remaining now that is inertia force which acts in opposite direction of acceleration a similar resistant due to 350 Newton we will get in the rightward direction therefore in opposite direction of acceleration I will add here Ma force means for inertia force now to find out this acceleration first we’ll find out R in here to find out Rn will apply equation along y-axis summation of FY equal to 0 assuming upward force is positive now what forces are acting here first one is RN next component of this 400 is what 400 sine 30 minus this is what 350 equal to what 0 that means normal reaction comes out to be 350 – 400 sine 30 that means this answer so to be worth 150 note now we’ll apply D alembert’s principle in horizontal direction that means if you apply equation along x axis to wate we get here summation of FX equal to 0 assuming rightward force is positive now which includes inertia forces therefore what we’ll get here component of 400 rightward plus 400 cos 30 frictional force minus 0.32 into RN inertia force again M into a equal to zero only three forces component of 400 then frictional force and Ma now this one is 400 of cos 30 minus 0.32 RN is 150 minus mass of box is not given weight is given therefore mass Ephrem to find out I take this wait divided by G means 9.81 into acceleration unknown term is only acceleration using calculate ripple calculate a comes out to be eight point three six four meters per second square using this acceleration if you’ll find out what is the velocity that V you are written as what u plus AT where u is zero and a into T that means four times a which is equal to 4 into 8 point 3 6 4 meter per second square that means what is the velocity of box is thirty three point four five meters per second this is nothing but final answer of this problem thank you