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")#