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March 15th, 2015, 09:54 PM   #1
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Math Focus: Certainty
Constant acceleration

Determine stopping distances for a car with initial speed of 95km/h and human reaction time 1.0s for an acceleration

a) $\displaystyle a = -5.0ms^{-2}$

I worked through it and got an answer of 135m

The answer is 94m. Need some help please.
I start my physics paper in a few months so trying to get a head start

Last edited by hyperbola; March 15th, 2015 at 09:59 PM.
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March 15th, 2015, 10:10 PM   #2
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Math Focus: Calculus/ODEs
I would first convert the initial speed to m/s:

$\displaystyle v_i=95\frac{\text{km}}{\text{hr}} \cdot\frac{1000\text{ m}}{1\text{ km}} \cdot\frac{1\text{ hr}}{3600\text{ s}}=\frac{475}{18}\,\frac{\text{m}}{\text{s}}$

So, we know that during the 1 second reaction time, the care traveled:

$\displaystyle d_r=\frac{475}{18}\,\text{m}$

Now, for a constant acceleration of $a$ (in meters per second per second), we may use:

$\displaystyle d_a=-\frac{v_i^2}{2a}$

So, for part a), we are given:

$\displaystyle a=-5\frac{\text{m}}{\text{s}^2}$

Hence:

$\displaystyle d_a=-\frac{\left(\frac{475}{18}\,\frac{\text{m}}{\text{ s}}\right)^2}{2\left(-5\frac{\text{m}}{\text{s}^2}\right)}=\frac{45125}{ 648}\text{ m}$

And thus the total stopping distance is:

$\displaystyle d=d_r+d_a=\frac{475}{18}\,\text{m}+\frac{45125}{64 8}\text{ m}=\frac{62225}{648}\text{ m}\approx96\text{ m}$
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