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A body travels 20 cm in the first 0.2 second and22 cm in the next 0.4 second. What will be the velocity at the end of the 0.7th second from start?(acceleration remains uniform)​

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Answer:

velocity at the end of 0.7sec from start would be 10cm/s

let initial velocity is u and acceleration is a.

case 1 : s₁ = 20 cm and t₁ = 0.2 sec

using formula, s₁ = ut₁ + 1/2 at₁²

⇒(20cm) = u × 0.2 + 1/2 × a × (0.2)²

⇒0.2 = 0.2u + 0.2 × 0.1 × a

⇒1 = u + 0.1a

⇒10 = 10u + a ............(1)

and velocity after 0.2 sec, v = u + at₁

= u + 0.2a

case 2 : s₂ = 22cm and t₂ = 0.4 sec

using formula, s₂ = vt₂ + 1/2 at₂²

⇒(22cm)² = (u + 0.2a) × (0.4) + 1/2 × a × (0.4)²

⇒0.22 = 0.4u + 0.08a + 0.08a

⇒0.22 = 0.4u + 0.16a

⇒11 = 20u + 8a ...........(2)

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

11 - 20 = 8a - 2a

⇒a = -9/6 = -3/2 = -1.5 m/s²

u = (10 - a)/10 = 11.5/10 = 1.15 m/s

velocity at the end of 0.7sec, v = u + a(0.7sec)

= 1.15 - 1.5 × 0.7

= 1.15 - 1.05

= 0.10

= 10cm/s

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