Four particles move along the x-axis with positions: Particle 1: x=3.5-2.7t³; Particle 2: x=3.5+2.7t³; Particle 3: x=3.5+2.7t²; Particle 4: x=3.5-3.4t-2.7t². Which have constant acceleration?
Options

Question

Four particles move along the x-axis with positions: Particle 1: x=3.5-2.7t³; Particle 2: x=3.5+2.7t³; Particle 3: x=3.5+2.7t²; Particle 4: x=3.5-3.4t-2.7t². Which have constant acceleration?

G1 Physics · Accepted Answer

Constant acceleration requires x(t) to be quadratic. Particles 3 and 4 have t² dependence only (plus constant/linear terms), so their accelerations are constant. Particles 1 and 2 contain t³ terms. Hence option D.