Question

In anticipation of a long 10 upgrade, a bus driver accelerates at a constant rate of 5 ft/s2 while still on a level section of a highway. Knowing that the speed of the bus was 80 mph as it begins to go upthe hill and that the driver doesnot change the setting on his throttle or shift gears, determine the distance traveled (in miles) by the bus upthe hill when its speed decreased to 50mph.Problem

Answer 1

Answer:

$S = 20903.4$ ft

Explanation:

First we will determine the acceleration of the bus while it is moving upward

The equilibrium  equation would be

$F - W sin\theta = ma'\\ma - W sin\theta = ma'\\m = \frac{W}{g} \\\frac{W}{g}*a - W sin\theta = \frac{W}{g} * a'\\\frac{a}{g} - sin\theta = \frac{a'}{g}\\\frac{x}{y} \frac{5}{32.2} - sin 10 = \frac{a'}{32.2} \\\a' = -0.59$

Let the displacement be $S_0$

As per newton's third law of motion

$v^2 -u^2 = 2as\\u = 80 \frac{mi}{h} = 117.33\frac{ft}{s}\\v = 50 \frac{mi}{h} = 73.33\frac{ft}{s}\\73.33 ^ 2 - 117.33^2 = 2 * (-0.59) * (S-S_0)\\\\S_0 = 0\\S = 20903.4$