# Need help calculating distance by a car

Linear, quadratic, module, parametric equations

### Need help calculating distance by a car

Cop says client was going 55mph on a road.

Client said she was going 40 mph

Client said she was at a red light and then accelerated so basically 0-40mph. She gave me the coordinates of the road.

So client went 0-40 in 528 feet (when cop saw her)

Cop says she was going 55mph so essentially 0-55mph in 528 feet.

My question is cops version possible, she drives a budget 2015 kia optima which goes 0-60 in 7.4-8.4 seconds per specs...im trying to call the officer a liar by way of saying what he saw was an impossibility or really unlikely.
Guest

### Re: Need help calculating distance by a car

Good morning.

Accordingly to specs of the car (I didn't check it, ok?), the cop could be right, at all!

Acceleration of the car: 0-60 mph in 7,4-8,4s, right?
Converting to feet per second (fps) = $$60 \cdot \dfrac{ 5280\text{feet}}{3600\text{seconds}}=88\; ft/s$$

Calculating two accelerations (7,4 and 8,4 seconds):
$$a_1=\dfrac{88}{7,4}=11,89ft/s^2\\a_2=\dfrac{88}{8,4}=10,48ft/s^2$$

These are the specs acceleration.

Now, let's calc the car acceleration during 528 feet.

If the car gets 55mph = $$55\cdot\dfrac{5280}{3600}\approx 80,67$$
Using the following equation:
$$v^2=v_0^2+2a\Delta s\\ 80,67^2=0^2+2a\cdot 528\\ 6\,507,6489=1\,056a\\ a=\dfrac{6\,507,6489}{1\,056}\\ a\approx 6,16ft/s^2$$

Totally possible!

In fact, the car could reach:
$$v^2=v_0^2+2a\Delta s\\ v^2=0^2+2(10,48)(528)\\ v^2=11\,066,88\\ v\approx 105,20ft/s=72,73mph$$

Hope have helped!
Guest

### Re: Need help calculating distance by a car

I wasn't logged in... Baltuilhe

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Joined: Fri Dec 14, 2018 3:55 pm
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