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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.