Question

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.

Answer 1

Using the second equation of motion: s = ut + \(\frac12\)at² 

where: s = distance covered 

u = initial velocity 

a = acceleration 

t = time = 4s 

Distance covered in 4s : 

s₁ = ut + \(\frac12\)at² 

s₁ = u × 4 + \(\frac12\)a × 4² 

s₁ = 4u + \(\frac{16}2\)a ………………… equation 1 

Distance covered in 5s: 

s₂ = ut + \(\frac12\)at² 

s₂ = u × 5 + \(\frac12\)a × 5²

s₂ = 5u +\(\frac{25}2\) a …………………… equation 2 

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

equation 2 – equation 1 

(s₂ – s₁ ) = (5u + \(\frac{25}2\)a ) - (4u + \(\frac{16}2\)a) 

(s₂ – s₁ ) = 5u – 4u + \(\frac{25}2\)a - \(\frac{16}2\)a) 

(s₂ – s₁ ) = u + \(\frac{9}2\)a