You know that your object starts from rest, which means that tis initial velocity will be equal to zero.
Moreover, it has an uniform acceleration of #4 "m/s"^2#. To determine its displacement, you can use this equation
#d = v_0 * t + 1/2 * a * t^2#, where
#t# - the object's time of travel;
#a# - its acceleration.
In your case, you have
#d = underbrace(v_0)_(color(blue)("=0")) * t + 1/2 * a * t^2 = 1/2 * a * t^2#
Point (1)
After 5 seconds, the object's displacement will be
#d = 1/2 * 4"m"/cancel("s"^2) * 5^2cancel("s"^2) = color(green)("50 m")#
Point (2)
To determine how much the object travelled in the #5^("th")# second of movement, you need to subtract the distance it travelled after 5 seconds from the distance it travelled after 6 seconds.
#Deltad_(5,6) = d_6 - d_5#
#d_6 = 1/2 * 4"m"/cancel("s"^2) * 6^2cancel("s"^2) = "72 m"#
#d_5 = "50 m"#
#Deltad_(5,6) = 72 - 50 = color(green)("22 m")#
Point (3)
The same method can be used to determine the distance the object travelled in its #8^("th")# second of movement.
#Deltad_(8,9) = d_9 - d_8#
#d_9 = 1/2 * 4"m"/cancel("s"^2) * 9^2cancel("s"^2) = "162 m"#
#d_8 = 1/2 * 4"m"/cancel("s"^2) * 8^2cancel("s"^2) = "128 m"#
Therefore,
#Deltad_(8,9) = 162 - 128 = color(green)("34 m")#
