Answer to Question #237871 in Molecular Physics | Thermodynamics for Kelani

Question

A rabbit is moving in the negative x-direction at 1.10 m/s when it spots a predator and accelerates to a velocity of 11.5 m/s along the positive y-axis, all in 1.40 s. Determine the x-component and the y-component of the rabbit's acceleration. (Enter your answers in m/s². Indicate the direction with the signs of your answers.)

(a)

x-component

 m/s²

(b)

y-component

 m/s²

Answer 1

First we have to consider the initial and final velocities to calculate the average acceleration:

$v_i= - \Big[ 1.10\frac{m}{s}\Big]\widehat{i} \\ v_f= \Big[ 11.5\frac{m}{s}\Big]\widehat{j} \\ \implies \Delta v=v_f-v_i \\ \implies \Delta v= [ 1.10\frac{m}{s}]\widehat{i} +[ 11.5\frac{m}{s}]\widehat{j} \text{ in an average time } \Delta t=1.40\,s.$

With the information we can calculate the average acceleration in terms of the x- and y-components:

$a=\Delta v/\Delta t= \dfrac{[ 1.10\frac{m}{s}]\widehat{i} +[ 11.5\frac{m}{s}]\widehat{j}}{1.40\,s} \\ \text{ } \\ \implies a= \big[ 0.786\frac{m}{s^2}\big]\widehat{i} + \big[ 8.214\frac{m}{s^2} \big]\widehat{j}$

In conclusion, (a) the x-component of the acceleration is +0.786 m/s² and (b) the y-component of the acceleration is +8.214 m/s².Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.