A particle moves according to v = u(1−x/L), starting from x=0. Which pair is correct?

Question

G1 Physics · Accepted Answer

The equation of motion is dx/dt = u(1−x/L). As x approaches L, the velocity approaches zero. Solving, 1−x/L = e⁻ᵘᵗᐟᴸ, so x=L is reached only as t→∞. Also, a = v dv/dx = u(1−x/L)(−u/L) = −(u²/L)(1−x/L). At x=L/2, a = −u²/(2L).