A particle moves in a straight line so that its displacement x at any time t is given by x² = 1 + t². Its acceleration at any time t is x⁻ⁿ where n = _____.

Question

G1 Physics · Accepted Answer

Given: x² = 1 + t² Differentiating: 2x(dx/dt) = 2t Therefore: xv = t Differentiate again: x(dv/dt) + v(dx/dt) = 1 xa + v² = 1 Since: v = t/x we have: v² = t²/x² Also: t² = x² - 1 Therefore: v² = (x² - 1)/x² = 1 - 1/x² Hence: xa = 1 - v² = 1/x² Therefore: a = 1/x³ = x⁻³ Thus: n = 3