Question

A particle moves along a straight line ox at a time t in second the distance x=40+12t-t'3 how long would the particle travel before coming rest

Answer 1

Answer:

Explanation:

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

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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

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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

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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 .

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hope this helps !