Answered: The kinematic equations can describe…

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter2: Motion In One Dimension

Section2.1: Average Velocity

Problem 2.1QQ: Under which of the following conditions is the magnitude of the average velocity of a particle...

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The kinematic equations can describe phenomena other than motion through space and time. Suppose x represents a person's bank account balance. The units of x would be dollars ($) and velocity v would give the rate at which the balance changes (in units of, for example, $/month). Acceleration would give the rate at which v changes. Suppose a person begins with five hundred dollars in the bank. Initial money management leads to no net change in the account balance so that
v0 = 0.
Unfortunately, management worsens over time so that
a = −2.57 ✕ 102 $/month2.
Assuming a is constant, find the amount of time in months until the bank account is empty.
months

Expert Solution

Step 1

Let, the person initial bank balance is ,

$x_{0} = 500 $$

and, A/Q, ${\frac{d x}{d t}}_{θ} = v_{0} = 0$

and the acceleration , means rate of change of V

which is cons.

a = $\frac{d v}{d t} = - 2.57 \times 10^{2} ($ / m o n t h^{2}) S o, v = - 2.57 \times 10^{2} t + e_{1}$

Here , e₁= constant which is evaluate from the boundary condition.

A/Q, at , t=0 , v=0 , so e₁=0

so, u= $\frac{d x}{d t} = - 2.57 \times 10^{2} \frac{t^{2}}{2} + e_{2}$

So , A/Q at t=0 , x= 500$

so e₂= 500$

$\Rightarrow x = 500 - \frac{2.57}{2} \times 10^{2} t^{2}$

we have to find the time in months so that his Bank balance is empty

Let say at t = to, x=0

So, 0 = 500 - 2.57/2 x10² t₀²

$\Rightarrow {t_{0}}^{2} = \frac{500 \times 2}{2.57 \times 100} = \frac{10}{2.57} = 3.891 t_{0} = 1.972$

So, It takes approximately 2 month to empty his balance in bank.

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