Question

position of a particle moving along x axis is given by X =6t-3t², where X is in m and t is in s. time(t) at which particle will momentarily come to rest is

a) ½ s
b) 2 s
c) 1 s
d) ¼ s​

Answer 1

Answer:

answer is option c) 1 second

Explanation:

velocity will be taken as zero because body came to rest

Answer 2

Concept:

Velocity can be defined as the differentiation of the position of the particle. When the velocity of the object comes to zero, the object will come to the rest.

Given:

The position of the particle, X = 6t-3t².

Find:

The time at which the particle will momentarily come to rest.

Solution:

Differentiating the position of the particle to calculate the velocity and substituting it to zero,

dX/dt = 0

dX/dt = d(6t-3t²)/dt

d(6t-3t²)/dt = 6 - 6t

6 - 6t = 0

6t = 6

t = 1 second

Hence, after 1 second the particle will momentarily come to rest when the position of a particle moving along the x-axis is X =6t-3t². Hence, the correct option is (c) 1 sec.

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