A particle moves along a straight line with velocity that is positive for and negative for

PHYSICS · Single correct · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

A particle moves along a straight line with velocity

v(t)

that is positive for

0\le t<4

and negative for

4\le t\le7

. Which of the following statements is true about its motion on the interval

0\le t\le7

? (a)

\displaystyle\int_{0}^{7}|v(t)|\,dt

equals the particle’s net displacement, and this value is strictly less than

\displaystyle\int_{0}^{7}v(t)\,dt

. (b)

\displaystyle\int_{0}^{7}v(t)^2\,dt

gives the particle’s total distance traveled because squaring makes the integrand non-negative. (c)

\displaystyle\int_{0}^{7}v(t)\,dt

equals the particle’s net displacement, and this value has smaller magnitude than

\displaystyle\int_{0}^{7}|v(t)|\,dt

. (d)

\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.