A 10kg mass moves along x-axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from x = 0 to x = 8 cm ?

(1) 8 × 10^–2 joules

(2) 16 × 10^–2 joules

(3) 4 × 10^–4 joules

(4) 1.6 × 10^–3 joules

A toy car of mass 5 kg moves up a ramp under the influence of force F plotted against displacement x. The maximum height attained is given by

1. y_max = 20 m

2. y_max = 15 m

3. y_max = 11 m

4. y_max = 5 m

The graph between the resistive force \(F\) acting on a body and the distance covered by the body is shown in the figure. The mass of the body is \(25\) kg and the initial velocity is \(2\) m/s. When the distance covered by the body is \(4\) m, its kinetic energy would be:

   
1.   \(50\) J
2. \(40\) J
3. \(20\) J
4.   \(10\) J

A particle of mass 0.1 kg is subjected to a force which varies with distance as shown in fig. If it starts its journey from rest at x = 0 , its velocity at x = 12 m is 

(1) 0 m/s

(2) $20\sqrt{2}m/s$

(3) $20\sqrt{3}m/s$

(4) 40 m/s

The relation between the displacement \(X\) of an object produced by the application of the variable force \(F\) is represented by a graph (as shown in the figure below). If the object undergoes a displacement from \(X=0.5\) m to \(X=2.5\) m the work done will be approximately equal to: 

    
1. 16 J
2. 32 J
3. 1.6 J
4. 8 J

A particle is given a constant horizontal velocity  from height h. Taking g to be constant every where, kinetic energy E of the particle w. r. t. time t is correctly shown in

(1)

(2)

(3)

(4)

The adjoining diagram shows the velocity versus time plot for a particle. The work done by the force on the particle is positive from

(1) A to B

(2) B to C

(3) C to D

(4) D to E

A particle which is constrained to move along the x-axis, is subjected to a force in the same direction which varies with the distance x of the particle from the origin as $F\left(x\right)=-kx+a{x}^3$. Here k and a are positive constants. For $x\ge 0$, the functional form of the potential energy U(x) of the particle is-

(1)

(2)

(3)

(4)

A force F acting on an object varies with distance x as shown here. The force is in newton and x in metre. The work done by the force in moving the object from x = 0 to x = 6 m is 

(1) 4.5 J

(2) 13.5 J

(3) 9.0 J

(4) 18.0 J

The potential energy of a system is represented in the first figure. the force acting on the system will be represented by:

1.		2.
3.		4.