Meriam, Kraige & Bolton — Kinematics of Particles: Problem 2_86

2/86 A particle moves on a circular path of radius $r = 0.8\text{ m}$ with a constant speed of $2\text{ m/s}$. The velocity undergoes a vector change $\Delta\vec{v}$ from $A$ to $B$. Express the magnitude of $\Delta\vec{v}$ in terms of $v$ and $\Delta\theta$ and divide it by the time interval $\Delta t$ between $A$ and $B$ to obtain the magnitude of the average acceleration of the particle for (a) $\Delta\theta = 30^\circ$, (b) $\Delta\theta = 15^\circ$, and (c) $\Delta\theta = 5^\circ$. In each case, determine the percentage difference from the instantaneous value of acceleration.