A particle moves along a straight line ox

Asked by admin @ 24/08/2021 in Physics viewed by 298 People

a particle moves along a straight line OX. At a time t[u = in seconds ] the distance x [in m] of the particle from O is given by x= 40+12t-t^3.how long would the particle travel before coming to rest?

Answered by admin @ 24/08/2021

At t=0 , particle is at , let's say x distance ,from O ;
then putting t=0 in the given displacement-time equation we get;
x =40 +12(0) -(0)³ = 40 m
___________________
Particle comes to rest that means velocity of particle becomes zero after travelling certain displacement ; let's say the time be t.
then after differentiating the given displacement-time equation wrt time we get velocity-time equation -->
v= 12-3t²
at time t =t (the time when the particle comes to rest ):
v= 0;
=> 12-3t² = 0;
=> t = 2 s
_____________________
Then ,at t =2s we are at , let's say x' distance from O ;
put this value of t (=2) in given displacement-time equation ,
we get;
x'= 40 +12(2) -(2)³;
= 56m
_____________________
Further;
We have seen that the particle started his journey when it is at 40m from the point O . And came to rest at 56m from the point O .
then the particle travelled a distance of :
56-40 = 16 meters .
_____________________
hope this helps !

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