Question 6

A particle starting at the origin, moves along the $x$-axis with velocity $v$ meters per second at time $0 \le t \le 5$ seconds given by the formula:

$$v = t - \frac{8}{t + 2}.$$

• Plot the velocity as a function of time and determine the intervals during which the particle is moving forward and the intervals during which the particle is moving backwards.
  
  
  
  
  
  
  
  
  
  
  
  
  
  
• Find the displacement of the particle from its initial position after five seconds.
  
  
  
  
  
  
  
  
  
  
  
• Find the total distance traveled by the particle in the first five seconds.