A particle moves in one dimension according to t = x² + x (in consistent units). Find acceleration a as a function of position x.
Options

Question

A particle moves in one dimension according to t = x² + x (in consistent units). Find acceleration a as a function of position x.

G1 Physics · Accepted Answer

Step 1: Differentiate t = x² + x with respect to x: dt/dx = 2x + 1. Step 2: Velocity is v = dx/dt = 1/(dt/dx) = (2x + 1)⁻¹. Step 3: Differentiate v(x): dv/dx = −2(2x + 1)⁻². Step 4: Acceleration a = dv/dt = v(dv/dx). Step 5: a = (2x + 1)⁻¹ × [−2(2x + 1)⁻²] = −2(2x + 1)⁻³. Final answer: a = −2/(2x + 1)³, Option B.