Question

a particle is moving on a curve path at any instant of time its velocity and acceleration are i - j and 2i+ j find the rate of change of speed respectively​

Answer 1

Answer:

The rate of change of speed would be  $\frac{1}{\sqrt{2} }$

Explanation:

The acceleration vector can be divided into two parts, one vector perpendicular to the velocity and one parallel to it. Hence,

a = X(i-j) + Y(i+j)

The component of a parallel to the velocity vector causes change in speed whereas component of acceleration perpendicular to velocity causes change in direction.

Solving for X and Y, in the equation

2i+j = X(i - j) + Y( i + j)

X + Y = 2

Y - X = 1

Hence X = 1/2 , Y= 3/2

$|\frac{dv}{dt} |$ = $|\frac{i-j}{2}|$ = $\frac{1}{\sqrt{2} }$  

Answer 2

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Explanation:

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