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Lesson Worksheet: Work and Integration Mathematics

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

Q1:

Complete the following: If a force given by 𝐹(𝑥) acts in the direction of the positive 𝑥-axis, then the work done by the force in moving a particle from 𝑥=𝑎 to 𝑥=𝑏, where 𝑎<𝑏 equals .

  • A𝐹(𝑥)𝑥d
  • B𝐹(𝑥)𝑥d
  • C𝐹(𝑥)2𝑥d
  • D𝐹(𝑥)𝑥d
  • E𝐹(𝑥)𝑥d

Q2:

True or False: If an object moves along a straight line by a varying force 𝑓(𝑥), then the work done 𝑊 to move the object from 𝑥=𝑎 to 𝑥=𝑏 is given by 𝑊=𝑓(𝑥)𝑥d.

  • AFalse
  • BTrue

Q3:

The figure shows the magnitude of a force acting on a body as it moves a distance 𝑑. Given that the force is measured in newtons and the distance is measured in meters, determine the work done in joules by the force to move the body from 𝑑=0 to 𝑑=7m.

Q4:

A body moves along the 𝑥-axis under the action of a force, 𝐹. Given that 𝐹=(8𝑠+12)N, where 𝑠 m is the displacement from the origin, determine the work done on the body by 𝐹 when the body moves from 𝑠=7m to 𝑠=8m.

Q5:

A variable force 𝐹, measured in newtons, is acting on a body, where 𝐹=3𝑠5. Find the work done by this force in the interval from 𝑠=4m to 𝑠=5m.

Q6:

A body moves along the 𝑥-axis under the action of a force 𝐹. Given that 𝐹=𝑥10N, where 𝑥()m is the displacement from the origin, determine the work done on the body by 𝐹 when the body moves from 𝑥=1m to 𝑥=2m.

  • A38 J
  • B34 J
  • C38 J
  • D34 J
  • E3 J

Q7:

A particle moves in a straight line under the action of the force 𝐹, where 𝐹=𝜋𝑆sin and 𝑆 is measured in meters. Calculate the work done by the force 𝐹 when the particle moves from 𝑆=0 to 𝑆=12.

  • A2 J
  • B12 J
  • C2𝜋 J
  • D32 J
  • E1𝜋 J

Q8:

A block moves in a straight line under the action of a force 𝐹=12𝑠+6𝑠+𝑐N, where 𝑠meters is the displacement of the body from its initial position. The work done by the force in moving the block from 𝑠=0m to 𝑠=3m is 34 J. Determine the work done by 𝐹 in moving the block from 𝑠=3m to 𝑠=6m.

Q9:

A body moves along the 𝑥-axis under the action of a force 𝐹. Given that 𝐹=2𝑥N, where 𝑥 m is the displacement from the origin, determine the work done on the body by 𝐹 when the body moves from 𝑥=1 to 𝑥=4.

  • A143 J
  • B28 J
  • C283 J
  • D283 J
  • E143 J

Q10:

A body moves along the 𝑥-axis under the action of a force 𝐹. Given that 𝐹=2𝑥N, where 𝑥 m is the displacement from the origin, determine the work done on the body by 𝐹 when the body moves from 𝑥=2 to 𝑥=3.

Approximate your answer to the nearest decimal place.

This lesson includes 28 additional questions and 179 additional question variations for subscribers.

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