At a particular instant velocity an...
Question
At a particular instant velocity and acceleration of a particle are (−i+j+2k)m/s and (3i−j+k)m/s2 respectively at the given instant particle's speed is :
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At a particular instant velocity and acceleration of a particle are ( (-hat{i}+hat{j}+2 hat{k}) m / s ) and ( (3 hat{i}-hat{j}+hat{k}) m / s^{2} ) respectively at the given instant particle's speed is :
A) increasing
(B) decreasing
(C) constant
(D) can't be say

JEE/Engineering Exams
Physics
Solution
12
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At a particular instant velocity and acceleration of a particle are (−i+j+2k)m/s and (3i−j+k)m/s2 respectively at the given instant particle's speed is :
Fullscreen

We can say by calculating the angle between
them. If it is between 0 and ( 90, ) we can say
that the celocity is increasing because some component of acceleration increases the
velocity, or else it will be decreasing.
( cos A=(a 1 a 2+b 1 b 2+c 1 c 2) / ) the sum of
magnitude of vectors
( cos A=4 /(2 sqrt{11}) )
( cos A=2 / sqrt{11} )
Thus A lies between 0 and 90 and thus its
velocity is increasing.

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