We are given graph of velocity v=f(t).
a) In the interval [0,1) and (5,7) velocity is positive.
So, it would move forward between 0 to 1 second and between 5 to 7 seconds.
In the interval (1,2) and (3,5) velocity is negative.
So, it would move backward between 1 to 2 second and between 3 to 5 seconds.
Slope in [0,2) and (6,7) is negative so, speed down between 0 to 2 and 6 to 7 seconds.
Slope between 3 and 6 seconds is positive so speed up between 3 to 6 seconds.
b) Slope in [0,2) and (6,7) is negative. So, acceleration 0 to 2 and 6 to 7 seconds are negative and
Slope between 3 and 6 seconds is positive. So acceleration between 3 to 6 seconds is positive.
Between 2 to 3 and 7 to 9 seconds velocity is constant. So, acceleration between 2 to 3 and 7 to 9 seconds is 0.
c) Slope between 3 and 6 seconds is positive so speed up between 3 to 6 seconds. So particle would move between 3 to 6 seconds.
d) Between 7 to 9 seconds velocity is 0. So, particle stand still between 7 to 9 seconds (7,9]