Question

A particle moving with uniform acceleration is found to travel 35 m in the 8th second 51m in the 12th second, its velocity in ms-1 at the beginning of the 11th second is

Answer 1

A particle moving with uniform acceleration is found to travel 35 m in the 8th second and  51m in the 12th second.

We have to find the velocity in m/s at the beginning of the 11th second.

Distance travelled in nth second is given by, Sₙ = u + a(2n - 1)/2.

where,

• u is initial velocity
• and a is acceleration.

step 1 : particle travels 35 m in 8th second.

so, S₈ = u + a(2 × 8 - 1)/2 = u + 7.5a = 35 ...(1)

step 2 : it travels 51m in 12th second.

so, S₁₂ = u + a(2 × 12 - 1)/2 = u + 11.5a = 51 ...(2)

from equations (1) and (2) we get,

a = 4 m/s² and u = 5 m/s

step 3 : we have to find the velocity at the beginning of the 11th second. it means, find the velocity at t = 10sec

i.e., v = u + at

= 5 + 4 × 10 = 45 m/s

Therefore the velocity of the particle at the beginning of the 11th second is 45 m/s.