A particle is moving with uniform acceleration covers a distance of 45

1.	A particle is moving with uniform acceleration covers a distance of 45 m in 6th second and 75 m in 12th second during its motion. Calculate the displacement of the particle after 20s?
Answer» S₆ = 45m, S₁₂= 75m using S_n = u + a(n – 1/2 ) i.e., S₆ = u + a or 45 = u + 5.5 a ……… (1) S₁₂= u + a(12 – 1/2) or 75 = u + a(11.5) …….. (2) Eq(2) – (1) gives 6 a = 30 Or a = 30/6 = 5 m/s² From (1), 45 = u + 5 × 5.5 u = 17.5 m/s. Distance travelled in t = 20s, S = ut + 1/2 at² = 17.5 × 20 + 1/2 × 5 × 20² =1350 m.

A particle is moving with uniform acceleration covers a distance of 45 m in 6th second and 75 m in 12th second during its motion. Calculate the displacement of the particle after 20s?

Answer»

S₆ = 45m, S₁₂= 75m

using S_n = u + a(n – 1/2 )

i.e., S₆ = u + a or 45 = u + 5.5 a ……… (1)

S₁₂= u + a(12 – 1/2) or 75 = u + a(11.5) …….. (2)

Eq(2) – (1) gives 6 a = 30

Or a = 30/6 = 5 m/s²

From (1), 45 = u + 5 × 5.5

u = 17.5 m/s.

Distance travelled in t = 20s,

S = ut + 1/2 at²

= 17.5 × 20 + 1/2 × 5 × 20²

=1350 m.