Question # 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 :

# 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

Solution

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.