A particle moves in the one-dimensional potential U(x) = x² + 4x + 10 J with total mechanical energy 15 J. If the turning points are x₁ and x₂, find |x₁ − x₂|.

Question

G1 Physics · Accepted Answer

At a turning point K=0, so U=E. Thus x²+4x+10=15 ⇒ x²+4x−5=0 ⇒ x=1 or −5. Therefore |x₁−x₂|=6.