SOLUTION: Jamie is jogging along the side of the road at a constant speed of 3 m/s. When she is 30 m from a bus stop, she sees that #301 bus has its blinker on and is departing from standsti

Question 824204: Jamie is jogging along the side of the road at a constant speed of 3 m/s. When she is 30 m from a bus stop, she sees that #301 bus has its blinker on and is departing from standstill with the acceleration of 2 m/s2. Jamie keeps running at the same speed. The question is will she catch up with the bus and if so � how long after she notices the bus and how far from the bus stop it will happen?

Answer by TimothyLamb(4379) (Show Source): You can put this solution on YOUR website!
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position at constant acceleration:
x = (1/2)at^2 + v0t + x0
position at constant velocity:
x = vt
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bus:
x = (1/2)at^2 + v0t + x0
v0 = 0
x0 = 30 m
a = 2 m/s^2
x = (1/2)2t^2 + 30
x = t^2 + 30
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Jamie:
x = vt
v = 3 m/s
x = 3t
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will Jamie catch the bus?
x = 3t = t^2 + 30
t^2 - 3t + 30 = 0
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the above quadratic equation is in standard form, with a=1, b=-3, and c=30
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
1 -3 30
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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this quadratic has two complex roots, which are:
y = 1.5 + (5.26782688)i
y = 1.5 - (5.26782688)i
the quadratic does not intercept the t-axis (the horizontal axis)
as such, there is no real-number solution to the problem
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graph:
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answer:
Jamie will not catch the bus
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Solve and graph linear equations:
https://sooeet.com/math/linear-equation-solver.php
---
Solve quadratic equations, quadratic formula:
https://sooeet.com/math/quadratic-formula-solver.php
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Solve systems of linear equations up to 6-equations 6-variables:
https://sooeet.com/math/system-of-linear-equations-solver.php
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