Question

A particle moves along a straight line OX. At a time t (in s Q. A particle moves along a straight line O X. At a time t (in second), the distance x (in metre) of the particle from O is given by x = 20+14t-t^3. How long would the particle travel before coming to rest? a) (3)^1/2 b) (5)^1/2 c) (8)^1/2 d) (18)^1/2

Answer 1

Answer:

Solution

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Correct option is

A

16m

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

=40m

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=12−3t

2

at time t=t (the time when the particle comes to rest ):

v=0;

=>12−3t

2

=0;

=>t=2s

Then ,at t=2s we are at , let's say x

′

distance from O;

put this value oft(=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 traveled a distance of:

56−40=16m.

Hence,

option (A) is correct answer.