Lesson Worksheet: Applications of Derivatives on Rectilinear Motion Mathematics • Higher Education
In this worksheet, we will practice applying derivatives to problems of motion in a straight line.
A particle moves along the . Its position from the origin is meters at a time seconds. The position is given by the equation . Find the times at which the particle’s velocity is equal to 0.
- A, where is an integer
- B, where is an integer
- C, where is an integer
- D, where is an integer
- E, where is an integer
A particle moves in a straight line, with respect to a stationary point, with position vector , where and is measured in seconds. is a unit vector parallel to the straight line, and is measured in meters.
Find the magnitude of the displacement vector after 2 s.
Find the total distance covered by the particle after 2 s.
Determine the magnitude of the average velocity vector of the particle between and .
Determine the average speed of the particle between and .
A particle started moving along the -axis. When the particle’s displacement from the origin is meters, its velocity is given by . Find the particle’s acceleration when its velocity vanished.