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

Quantrex Academy · Accepted Answer

Correct answer: A. 16 ~m

The given equation is x=40+127-t^3 Differentiating we get u=(d x)/(d t)=12-3 t^2 When particle comes to rest means array l & v = 0 & 12-3 t^2 =0 & t =2 sec . array The distance travelled before coming to rest aligned ∫_0^5 d s & = _0^2 v d t 5 & =∫_0^2(12-3 t^2) d t & =[12 t-(3 t^3)/(3)]_0^2 & =12 × 2-(8-0) & =16 ~m . aligned

A particle moves along a straight line OX . At a time t (in...

Options

Correct answer

Step-by-step solution

More from Motion in One Dimension