Let \(\vec{v}\) and \(\vec{a}\) be instantaneous velocity and the acceleration respectively of a particle moving in a plane. The rate of change of speed (dv/dt) of the particle is:

(a) \(|a|\)

(b) \((v.a)/|v|\)

(c) the component of \(\vec{a}\) in the direction of \(\vec{v}\)

(d) the component of \(\vec{a}\) perpendicular to \(\vec{v}\)

**Solution:**

Let us consider \(v^2=v_x^2+v_y^2\).

We differentiate the above equation.

\(\frac{dv}{dt}\)=\((v_xa_x+v_ya_y)v\)=\(\frac{v.a}{v}\).

Hence, the correct option will be B along with C since the component of a is in the direction of v.