A particle with constant non-zero acceleration passes the same position at times t₁ and t₂. Which statements are necessarily correct?
Select all that apply

Question

A particle with constant non-zero acceleration passes the same position at times t₁ and t₂. Which statements are necessarily correct?

G1 Physics · Accepted Answer

For constant acceleration, x(t)=x₀+ut+at²/2. If the same position is reached at t₁ and t₂, these are the two roots of a quadratic equation in time. The vertex of the parabola lies at the average of the roots: turning time = (t₁+t₂)/2. At the vertex, v=0. Since velocity varies linearly with time, the endpoint velocities are equal in magnitude and opposite in sign. Acceleration remains the same non-zero constant throughout. Thus A, B and C are correct.