Obtain a relation for the distance travelled by an object moving with a uniform acceleration in the interval between 4^th and 5^th second.

Using the second equation of motion: s = ut + at²

where: s = distance covered
u = initial velocity
a = acceleration
t = time = 4s

Distance covered in 4s :

s₁ = ut + at²
s₁ = u × 4 + a × 4²
s₁ = 4u + a ………………… equation 1

Distance covered in 5s:

s₂ = ut + at²
s₂ = u × 5 + a × 5²
s₂ = 5u + a …………………… equation 2

Distance travelled by an object between 4^th and 5^th sec:

equation 2 – equation 1
(s₂ – s₁ ) = (5u + a ) - (4u + a)
(s₂ – s₁ ) = 5u – 4u +a - a)
(s₂ – s₁ ) = u + a