Question

2. A particle moving with a uniform acceleration travels 24 metres and 64 metres in first to successive intervals
of 4 seconds each its initial velocity is
(1) 2 m/s
(2) 1 m/s
(3) 5 m/s
(4)10m/s​

Answer 1

Given that, a particle is moving with a uniform acceleration and travels 24 m & 64 m into first two successive intervals for 4 seconds each.

We have to find the initial velocity.

There are total two cases, in first case it travels 24 m in 4 sec and in second case it travels 64 m in 4 sec.

Case 1)

s = ut + 1/2 at²

→ 24 = u(4) + 1/2 × a × (4)²

→ 24 = 4u + 1/2 × 16a

→ 24 = 4u + 8a

→ 24 - 8a = 4u ...........(1st equation)

Case 2)

S = ut + 1/2 at²

Now, after 4 sec. v = u + at

v = u + a(4) = u + 4a

→ 64 = (u + 4a)(4) + 1/2 × a × (4)²

→ 64 = 4u + 16a + 1/2 × 16a

→ 64 = 4u + 16a + 8a

→ 64 = 4u + 24a

→ 64 - 24a = 4u .........(2nd equation)

On comparing, (1st equation) and (2nd equation) we get,

→ 24 - 8a = 64 - 24a

→ 64 - 24 = -8a + 24a

→ 40 = 16a

→ 2.5 = a

(Acceleration = 2.5 m/s²)

Substitute value of a in (1st equation)

→ 24 - 8(2.5) = 4u

→ 24 - 20 = 4u

→ 4 = 4u

→ 1 = u

Therefore, the initial velocity is 1 m/s.

Option (2) 1 m/s.