A particle moves along a line with velocity meters per second for

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

Problem

A particle moves along a line with velocity v(t)=cos⁡t−t2v(t)=\cos t-\dfrac{t}{2} meters per second for 0≤t≤50\le t\le 5. Let a(t)a(t) denote its acceleration. Which of the following times is closest to when the particle is momentarily at rest and then begins moving in the negative direction (that is, v(t)=0v(t)=0 and a(t)<0a(t)<0)? (a) t≈1.57 st\approx 1.57\text{ s} (b) t≈1.1 st\approx 1.1\text{ s} (c) t≈0.74 st\approx 0.74\text{ s} (d) t≈3.67 st\approx 3.67\text{ s}

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