A particle moves along a straight line OX . At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12 t – t 3 . How long would the particle travel before coming to rest?

Question

A particle moves along a straight line OX . At a time t (in seconds) the distance x (in metres) of the particle from O is given by x = 40 + 12 t – t 3 . How long would the particle travel before coming to rest?, 16 m, 24 m, 40 m, 56 m

MARKS App · Accepted Answer

x = 40 + 12 t – t 3 ∴ Velocity, v = d x d t = 1 2 - 3 t 2 When particle come to rest, d x d t = v = 0 ∴ 12 – 3 t 2 = 0 ⇒ 3 t 2 = 12 ⇒ t = 2 s . Distance travelled by the particle before coming to rest, x i = 40 t = 0 x f = 40 + 24 - 8 f o r t = 2 s x f - x i = 16 m

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