Question

A boy cover 12 m
in 2nd second and 20 m in 4th sec. How much distance it will cover in 4
sec?​

Answer 1

Given :

A boy covers 12m in 2nd second and 20m in 4th second.

To Find :

Distance covered by boy in four seconds$.$

Solution :

❇ Distance covered by object in nth second of journey is given by

• Sₙ = u + a/2 [2n - 1]

Sₙ denotes distance

u denotes initial velocity

a denotes acceleration

n denotes no. of second

⧪ Distance covered in 2nd second :

⭆ S₂ = u + a/2 [2(2) - 1]

⭆ 12 = u + a/2 [4 - 1]

⭆ 12 = u + 3a/2 .......... (i)

⧪ Distance covered in 4th second :

⭆ S₄ = u + a/2 [2(4) - 1]

⭆ 20 = u + a/2 [8 - 1]

⭆ 20 = u + 7a/2 .......... (ii)

On solving both equations, we get

• a = 4 m/s²
• u = 6 m/s

Now applying second equation of kinematics;

➠ d = ut + 1/2 at²

➠ d = (6)(4) + 1/2 [4 × 4²]

➠ d = 24 + 1/2 (4 × 16)

➠ d = 24 + 64/2

➠ d = 24 + 32

➠ d = 56 m