rectilinear motion example particle decelerating

The video tutorial explains a motion problem involving a particle decelerating along a straight line. The problem is modeled using the equation of acceleration as a function of velocity. The tutorial provides a practical example using a runner to illustrate the concept. It then walks through solving the problem using integration and boundary conditions to find the time and distance when the velocity is a fraction of its initial value. Key mathematical skills such as integration and differentiation are applied throughout the solution.

How is the integration constant C determined in the context of this problem?

What is the final equation that describes the motion of the particle?

Calculate the time when the velocity is 0.4 meters per second.

What is the distance traveled by the particle when its velocity is 0.4 meters per second?