A particle is acted upon by the time-dependent force F = (6t, 4) N from t = 0 to t = 2 s. If the magnitude of the impulse is 4√N N·s, find N.

Question

G1 Physics · Accepted Answer

Impulse is the time integral of force. For the x-component, Jx = ∫₀² 6t dt = [3t²]₀² = 12 N·s. For the y-component, Jy = ∫₀² 4 dt = 8 N·s. Therefore the impulse vector is J = (12, 8) N·s. Its magnitude is |J| = √(12²+8²) = √208 = 4√13 N·s. Hence N = 13.