For a particle that moves along a line with velocity on the interval

MATHEMATICS · Single correct · A Level · Mathematics · Kinematics · Kinematics

Problem

For a particle that moves along a line with velocity v(t)v(t) on the interval [a,b][a,b], which of the following integrals represents the total distance traveled during that interval? (a) 12∫ab∣v(t)∣ dt\displaystyle \tfrac12\int_a^b |v(t)|\,dt (b) ∫ab∣v(t)∣ dt\displaystyle \int_a^b |v(t)|\,dt (c) ∫abv(t) dt\displaystyle \int_a^b v(t)\,dt (d) ∣∫abv(t) dt∣\displaystyle \left|\int_a^b v(t)\,dt\right|

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