An object of mass \(500\) g initially at rest is acted upon by a variable force whose x-component varies with \(x\) in the manner shown. The velocities of the object at the points \(x=8\) m and \(x=12\) m would have the respective values of nearly:

Force \(F\) on a particle moving in a straight line varies with distance \(d\) as shown in the figure. The work done on the particle during its displacement of \(12\) m is: 

              

A body of mass 3 kg is under a constant force which causes a displacement s in metres in it, given by the relation s = $\frac{1}{3}$ t², where t is in sec. Work done by the force in 2 sec is:

1. $\frac{5}{19}J$

2. $\frac{3}{8}J$

3. $\frac{8}{3}J$

4. $\frac{19}{5}J$

\(300 ~\text{J}\) of work is done in sliding a \(2~\text{kg}\) block up an inclined plane of height \(10~\text{m}\). Taking \(g=\) \(10\) m/s², work done against friction is:
1. \(200 ~\text{J}\)
2. \(100 ~\text{J}\)
3. \(\text{zero}\)
4. \(1000 ~\text{J}\)

A force \(F\) acting on an object varies with distance \(x\) as shown below:

The force is in Newton and \(x\) is in meters. The work done by the force in moving the object from \(x = 0\) to \(x = 6\) m is:
1. \(18.0\) J
2. \(13.5\) J
3. \(4.5\) J
4. \(9.0\) J