Answer to Question #83397 in Mechanics | Relativity for Geetha

Question

particle moving with uniform acceleration along x axis at x1 = 10 and x2 = 20 at t = 6 and t = 10 respectively. If its velocity at t = 6 is 0.5 m/s it acceleration is

Answer 1

Answer on Question # 83397, Mechanics/ Relativity

particle moving with uniform acceleration along x axis at x1 = 10 and x2 = 20 at t = 6 and t = 10 respectively. If its velocity at t = 6 is 0.5 m/s it acceleration is

Solution

v₂ = v₁ + at

v₂² = v₁² + 2aΔx

Then

(v₁ +at)² = v₁² + 2aΔx (1)

where

Δx= x₂ - x₁ = 20-10= 10 m

Δt = t₂ - t₁ =10-6 = 4 s

v₁ = 0.5 m/s

v₂ = 0.5 + a*4

Solve equation (1)for a:

(0.5 + a*4)² = (0.5)² + 2a*10

(0.5 + a*4)² -(0.5)² = 2a*10

(0.5+4a-0.5)(0.5+4a+0.5) =20a

4a(1+4a)=20a

1+4a =5

a=1 (m/s²)

Answer: a=1 (m/s²)