Answer:
The detailed calculations are shown below;
Explanation:
a)The maximum acceleration of the particle:
 It is seen that the maximum change in velocity is at the time between 8s to 10s.
       Maximum acceleration: [tex]\frac{V}{t}[/tex]
                          = [tex]\frac{20}{2}[/tex]
                          = 10 m/[tex]s^{2}[/tex]
b) The deceleration of the particle
     The velocity of particle is decreased after 10s so,
           deceleration = - [tex]\frac{40}{6}[/tex]
                      = - 6.67 m/[tex]s^{2}[/tex]
c)The total distance traveled by the particle = Area under the curve
                = [tex]\frac{1}{2}[/tex]* 4*20 + 4*20 +  [tex]\frac{1}{2}[/tex]* 2*20+ 2*20+ [tex]\frac{1}{2}[/tex]* 40*16
                            = 290 m
d)The average velocity of the particle = [tex]\frac{Area under the curve}{Total time}[/tex]
                                = [tex]\frac{290}{16}[/tex]
                                = 18.12 m/s
