# Worksheet: Work and Integration

In this worksheet, we will practice using integration to find the work done by a variable force.

**Q2: **

A body moves along the -axis under the action of a force, . Given that , where m is the displacement from the origin, determine the work done on the body by when the body moves from to .

**Q3: **

From Newtonβs universal gravitational law, we know that a body at a distance from the center of Earth is affected by a gravitational force such that , where is a constant. Assuming the radius of Earth is 6,371 km, find the magnitude of the work required for a satellite of mass 793 kg to achieve vertical takeoff from the ground and reach orbit at an altitude of 831 km.

**Q4: **

A particle is moving in a straight line under the action of a force given by where the force is measured in newtons and the displacement is measured in meters. Calculate the work done by the force when the particle moves from to .

- A-2 joules
- B4 joules
- C-6 joules
- D joules

**Q5: **

The figure shows the relation between a force , measured in newtons, acting on a body and the distance , in metres, travelled by that body. Determine the work done between and .

**Q6: **

A block moves in a straight line under the action of a force , where meters is the displacement of the body from its initial position. The work done by the force in moving the block from to is 34 J. Determine the work done by in moving the block from to .

**Q7: **

A variable force , measured in newtons, is acting on a body, where . Find the work done by this force in the interval from to .

**Q8: **

A particle is moving in a straight line under the action of a constant force of magnitude 47 N acting in the direction of motion. The displacement of the particle is given by the relation , where is a unit vector parallel to the direction of motion. Given that the displacement is measured in metres, find the work done, in joules, by this force in the first 9 seconds of motion.

**Q9: **

A particle moves in a straight line under the action of the force , where and is measured in meters. Calculate the work done by the force when the particle moves from to .

- A50
- B100
- C
- D25

**Q10: **

A particle moves in a straight line under the action of the force , where and is measured in meters. Calculate the work done by the force when the particle moves from to .

- A2 J
- B J
- C J
- D J
- E J