Question

A particle moves with deceleration along the circle of radius $R$ so that at any moment of time its tangential and centripetal accelerations are equal in moduli. At the initial moment $t=0$, the speed of the particle equals $v_0$. Then

The total acceleration of the particle is

• A. $a=\frac{\sqrt{2}{v}^2}{R}$
• B. $a=\frac{\sqrt{2}v}{R}$
• C. $a=\frac{\sqrt{2}R}{v}$
• D. $a=\frac{2R}{v}$

Answer 1

The correct option is A $a=\frac{\sqrt{2}{v}^2}{R}$

$\begin{array}{cc}{a}_{\text{total}}& =\sqrt{{\left|a_{\text{tan}}\right|}^2+{\left|a_{rad}\right|}^2}\\ & =\sqrt{{\left|a_{rad}\right|}^2+{\left|a_{rad}\right|}^2}\\ & =\sqrt{2}{a}_{rad}\\ & =\frac{\sqrt{2}{v}^2}{R}\end{array}$