Physics

Physics

Problem

A particle moves along a straight line with velocity v(t)v(t) that is positive for 0≤t<40\le t<4 and negative for 4≤t≤74\le t\le7. Which of the following statements is true about its motion on the interval 0≤t≤70\le t\le7? a) ∫07∣v(t)∣ dt\displaystyle\int_{0}^{7}|v(t)|\,dt equals the particle’s net displacement, and this value is strictly less than ∫07v(t) dt\displaystyle\int_{0}^{7}v(t)\,dt. b) ∫07v(t)2 dt\displaystyle\int_{0}^{7}v(t)^2\,dt gives the particle’s total distance traveled because squaring makes the integrand non-negative. c) ∫07v(t) dt\displaystyle\int_{0}^{7}v(t)\,dt equals the particle’s net displacement, and this value has smaller magnitude than ∫07∣v(t)∣ dt\displaystyle\int_{0}^{7}|v(t)|\,dt. d) ∫07v(t) dt\displaystyle\int_{0}^{7}v(t)\,dt equals the particle’s total distance traveled because the particle’s velocity is never zero on the interval.

Browse the problem library