Applications of derivatives: Motion along a line

The  exercise appears under the Differential calculus Math Mission. This exercise practices the position, velocity and acceleration of particles along a line.

Types of Problems
There are two types of problems in this exercise:


 * 1) Answer the problem about the particle: This problem provides the rule for a particle in motion. The student is expected to use the function to determine some answers about the particle.Aodmaal1.png
 * 2) Use the graphs to answer the questions: This problem provides several graphs that represent the position, velocity and acceleration of a particle in motion. The student is expected to use the graphs to answer some associated questions.Aodmaal2.png

Strategies
Knowledge of derivatives and rectilinear motion are encouraged to ensure success on this exercise.
 * 1) The original function, called s(t), generally represents the position of a particle.
 * 2) The velocity of a particle is the derivative of the position, i.e., v(t)=s'(t).
 * 3) Acceleration is the second derivative of position, i.e., a(t)=v'(t)=s''(t).
 * 4) When acceleration and velocity are positive, a particle is moving forward and speeding up.
 * 5) When acceleration is positive and velocity is negative, a particle is moving back and slowing down.
 * 6) When acceleration is negative and velocity is positive, a particle is moving forward and slowing down.
 * 7) When both are negative, a particle is moving back and speeding up.

Real-life Applications

 * 1) Most of the problems in this subsection are applications in some sense, so the majority of the exercises are applications also.