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

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

Problem

A particle moves along a line with velocity v(t)=At+Bv(t)=At+B meters per second for 0≤t≤60\le t\le 6 seconds. During this time the particle’s displacement is 1212 meters and the total distance it travels is 1818 meters. Which of the following ordered pairs (A,B)(A,B) satisfies these conditions? (a) (−3+53,  5−5)\displaystyle\left(\dfrac{-3+\sqrt5}{3},\;5-\sqrt5\right) (b) (−23,  4)\left(-\dfrac23,\;4\right) (c) (−3−53,  5+5)\displaystyle\left(\dfrac{-3-\sqrt5}{3},\;5+\sqrt5\right) (d) (−1,  5)(-1,\;5)

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