Question

A particle moves along a straight line OX. At a time t (in second) the distance x (in metre) of the particle from O is given by x = 40 + 12t – t3. How long would the particle travel before coming to rest?

(a) 24 m

(b) 40 m

(c) 56 m

(d) 16 m

Answer 1

Correct option (c) 56m

Explanation:

When particle comes to rest

V = 0 = dx/dt = d/dx(40 + 12t - t3)

⇒ 12 - 3t2 = 0

⇒ t2 = 12/3 = 4 ∴ t = 2sec

Therefore distance travelled by particle before coming to rest,

x = 40 + 12t – t3 = 40 + 12 × 2 – (2)3 = 56m