A particle has acceleration a=αx. At x=0 its speed is u. Its speed when it reaches x=L is:
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A particle has acceleration a=αx. At x=0 its speed is u. Its speed when it reaches x=L is:

G1 Physics · Accepted Answer

Use a = v dv/dx = αx. Then v dv = αx dx. Integrating from x=0, v=u to x=L, v=v at x=L, (v at x=L²−u²)/2 = αL²/2. Therefore v at x=L² = u² + αL², so v at x=L = √(u²+αL²).