Lesson: Rectilinear Motion and Integration Mathematics • Higher Education

In this lesson, we will learn how to apply integrals to solve problems involving motion in a straight line.

Lesson Plan

Students will be able to

find the change in the velocity of a particle over a certain time period when given the acceleration function, ,
find the velocity function of a particle, , when given the acceleration function, , and an initial condition:
- extend this to find the instantaneous velocity at a certain time,
find the displacement of a particle over a certain time period when given the velocity function, ,
find the displacement function, , when given the velocity function, , and an initial condition:
- extend this to find displacement at a certain time.

Lesson Presentation

Lesson Video

Lesson Explainer

Lesson Playlist

06:55
03:31
+6

04:58

Lesson Worksheet

Q1:

A car, starting from rest, began moving in a straight line from a fixed point. Its velocity after seconds is given by Calculate the displacement of the car when .

Q2:

A particle is moving in a straight line such that its velocity at time seconds is given by . Given that its initial position is 20 m, find an expression for its position at time seconds.

Q3:

A particle is initially at rest at the origin. It starts to move along the -axis such that at time seconds, its velocity is given by What is the particle’s displacement when it comes to instantaneous rest?