Q.1 (e) The acceleration of a particle in rectilinear motion is given by a = 100 - 3x²\ m/s² . Knowing that at t = 0, v = 0 and x = 0 find the velocity of the particle at x = 8 m.

Since a is a function of x, use a = vdv/dx : v dv = (100 - 3x²) dx ⇒ displaystyle∫₀^v v dv = ∫₀^x (100 - 3x²) dx v²/2 = 100x - x³ At x = 8 m: v²/2 = 800 - 512 = 288 ⇒ v² = 576 Answer: v = 24 m/s at x = 8 m.

The acceleration of a particle in rectilinear motion is given by \(a = 100 - 3x^2\ \text{m/s}^2\). Knowing that at t = 0, v = 0 and x = 0 find the velocity of the particle at x = 8 m.

Q.1 (e) The acceleration of a particle in rectilinear motion is given by \(a = 100 - 3x^2\ \text{m/s}^2\). Knowing that at t = 0, v = 0 and x = 0 find the velocity of the particle at x = 8 m.

Doubtly Asked 25 Oct 2026 mu engineering Save WhatsApp Report

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Since a is a function of x, use \(a = v\dfrac{dv}{dx}\):

\(v\,dv = (100 - 3x^2)\,dx \Rightarrow \displaystyle\int_0^v v\,dv = \int_0^x (100 - 3x^2)\,dx\)

\(\dfrac{v^2}{2} = 100x - x^3\)

At x = 8 m: \(\dfrac{v^2}{2} = 800 - 512 = 288 \Rightarrow v^2 = 576\)

Answer: v = 24 m/s at x = 8 m.

Doubtly AI · 25 Oct 2026 AI-verified · Oct 2026 Report

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The acceleration of a particle in rectilinear motion is given by \(a = 100 - 3x^2\ \text{m/s}^2\). Knowing that at t = 0, v = 0 and x = 0 find the velocity of the particle at x = 8 m.

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