A particle moves under a = −k/x². At x=r₀ its speed is u. At another position r its speed v satisfies:

Question

G1 Physics · Accepted Answer

Use v dv/dx = −k/x². Therefore v dv = −k x⁻² dx. Integrating from r₀,u to r,v, (v²−u²)/2 = k(1/r − 1/r₀). Hence v² = u² + 2k(1/r − 1/r₀).