Question

At a particular instant velocity and acceleration of a particle are $(-\hat{i}+\hat{j}+2\hat{k})m/s$ and $(3\hat{i}-\hat{j}+\hat{k})m/s$ respectively at the given instant particle's speed is:

• A. increasing
• B. decreasing
• C. constant
• D. can't be say

Answer 1

The correct option is A increasing

We can say by calculating the angle between them$.$ If it is between $0$ and $90,$ we can say that the velocity is increasing because some component of acceleration increases the velocity$,$ or else it will be decreasing$.$

$\cos A=\frac{\left(a_1{a}_2+b_1{b}_2+c_1{c}_2\right)}{thesumofmagnitudeofvectors}$

$\cos A=\frac{4}{\left(2\sqrt{11}\right)}$

$\cos A=\frac{2}{\sqrt{11}}$

Thus $A$ lie between $0$ and $90$ and thus its velocity is increasing$.$

Hence,

option $\left(A\right)$ is correct answer.